St Petersburg Mathematical Journal最新文献

{"title":"Discrete Schrödinger operators with decaying and oscillating potentials","authors":"R. Frank, S. Larson","doi":"10.1090/spmj/1803","DOIUrl":"https://doi.org/10.1090/spmj/1803","url":null,"abstract":"<p>The paper is devoted to a family of discrete one-dimensional Schrödinger operators with power-like decaying potentials with rapid oscillations. In particular, for the potential <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V left-parenthesis n right-parenthesis equals lamda n Superscript negative alpha Baseline cosine left-parenthesis pi omega n Superscript beta Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>V</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>λ<!-- λ --></mml:mi> <mml:msup> <mml:mi>n</mml:mi> <mml:mrow> <mml:mo>−<!-- − --></mml:mo> <mml:mi>α<!-- α --></mml:mi> </mml:mrow> </mml:msup> <mml:mi>cos</mml:mi> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>π<!-- π --></mml:mi> <mml:mi>ω<!-- ω --></mml:mi> <mml:msup> <mml:mi>n</mml:mi> <mml:mi>β<!-- β --></mml:mi> </mml:msup> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">V(n)=lambda n^{-alpha }cos (pi omega n^beta )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"1 greater-than beta greater-than 2 alpha\"> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>&gt;</mml:mo> <mml:mi>β<!-- β --></mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>2</mml:mn> <mml:mi>α<!-- α --></mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">1&gt;beta &gt;2alpha</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, it is proved that the spectrum is purely absolutely continuous on the spectrum of the Laplacian.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140942122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Circuit synthesis based on a prescribed Lagrangian","authors":"A. Figotin","doi":"10.1090/spmj/1801","DOIUrl":"https://doi.org/10.1090/spmj/1801","url":null,"abstract":"<p>On the basis of a prescribed quadratic Lagrangian, an algorithm of synthesis for an electric circuit is suggested here. That is, the circuit evolution equations are equivalent to the relevant Euler–Lagrange equations. The proposed synthesis is a systematic approach that allows one to realize any finite-dimensional physical system described by a quadratic Lagrangian in a lossless electric circuit so that their evolution equations are equivalent. The synthesized circuit is composed of (i) capacitors and inductors of positive or negative values for the respective capacitances and inductances, and (ii) gyrators. The circuit topological design is based on the set of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L upper C\"> <mml:semantics> <mml:mrow> <mml:mi>L</mml:mi> <mml:mi>C</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">LC</mml:annotation> </mml:semantics> </mml:math> </inline-formula> fundamental loops (f-loops) that are coupled by <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G upper L upper C\"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:mi>L</mml:mi> <mml:mi>C</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">GLC</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-links each of which is a serially connected gyrator, capacitor, or inductor. The set of independent variables of the underlying Lagrangian is identified with f-loop charges defined as the time integrals of the corresponding currents. The EL equations for all f-loops account for the Kirchhoff voltage law whereas the Kirchhoff current law is fulfilled naturally as a consequence of the setup of the coupled f-loops and the corresponding charges and currents. In particular, the proposed synthesis provides for efficient implementation of the desired spectral properties in an electric circuit. The synthesis provides also a way to realize arbitrary mutual capacitances and inductances through elementary capacitors and inductors of positive or negative respective capacitances and inductances.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Resolvent stochastic processes","authors":"I. Ibragimov, N. Smorodina, M. Faddeev","doi":"10.1090/spmj/1797","DOIUrl":"https://doi.org/10.1090/spmj/1797","url":null,"abstract":"<p>A family <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"r Subscript lamda\"> <mml:semantics> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>λ<!-- λ --></mml:mi> </mml:msub> <mml:annotation encoding=\"application/x-tex\">r_lambda</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"lamda element-of double-struck upper C\"> <mml:semantics> <mml:mrow> <mml:mi>λ<!-- λ --></mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mrow> <mml:mi mathvariant=\"double-struck\">C</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">lambda in mathbb {C}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, of complex stochastic processes is introduced, which makes it possible to construct a probabilistic representation for the resolvent of the operator <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"minus one half StartFraction d squared Over d x squared EndFraction\"> <mml:semantics> <mml:mrow> <mml:mo>−<!-- − --></mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mfrac> <mml:msup> <mml:mi>d</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mrow> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>x</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:mfrac> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">-frac {1}{2}frac {d^2}{dx^2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. For <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"lamda equals 0\"> <mml:semantics> <mml:mrow> <mml:mi>λ<!-- λ --></mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">lambda =0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the process <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"r Subscript lamda\"> <mml:semantics> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>λ<!-- λ --></mml:mi> </mml:msub> <mml:annotation encoding=\"application/x-tex\">r_lambda</mml:annotation> </mml:semantics> </mml:math> </inline-formula> coincides with the Brownian local time process.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Functions of perturbed noncommuting unbounded selfadjoint operators","authors":"A. Aleksandrov, V. Peller","doi":"10.1090/spmj/1784","DOIUrl":"https://doi.org/10.1090/spmj/1784","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=\"application/x-tex\">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a function on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper R squared\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {R}^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in the inhomogeneous Besov space <inline-formula content-type=\"math/tex\"> <tex-math> {text textit {Russian {B}}}_{infty ,1}^{1}(mathbb {R}^2)</tex-math></inline-formula>. For a pair <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper A comma upper B right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>A</mml:mi> <mml:mo>,</mml:mo> <mml:mi>B</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(A,B)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of not necessarily bounded and not necessarily commuting self-adjoint operators, the function <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f left-parenthesis upper A comma upper B right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>A</mml:mi> <mml:mo>,</mml:mo> <mml:mi>B</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">f(A,B)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A\"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=\"application/x-tex\">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper B\"> <mml:semantics> <mml:mi>B</mml:mi> <mml:annotation encoding=\"application/x-tex\">B</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is introduced as a densely defined linear operator. It is shown that if <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"1 less-than-or-equal-to p less-than-or-equal-to 2\"> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>p</mml:mi> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">1le ple 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deformations of commutative Artinian algebras","authors":"A. Aleksandrov","doi":"10.1090/spmj/1783","DOIUrl":"https://doi.org/10.1090/spmj/1783","url":null,"abstract":"<p>The paper is devoted to the study of deformations of Artinian algebras and zero-dimensional germs of varieties. In particular, an approach is developed to solving the open problem about the nonexistence of rigid Artinian algebras; it is based essentially on the use of the canonical duality in the cotangent complex. Thus, it is shown that there are no rigid Gorenstein Artinian algebras and rigid almost complete intersections. The proof of the latter statement is based on the properties of the torsion functors. More precisely, the tensor product of the conormal and canonical modules of the corresponding Artinian algebra is calculated. In this case, the homology and cohomology groups of higher degrees are also found. Among other things, some estimates are obtained for the dimension of the spaces of the first lower and upper cotangent functors of Artinian algebras, and the relationship between them is described. In conclusion, several examples of nonsmoothable Artinian noncomplete intersections are examined, and some unusual properties of such algebras are discussed.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On extra zeros of 𝑝-adic Rankin–Selberg 𝐿-functions","authors":"D. Benois, S. Horte","doi":"10.1090/spmj/1785","DOIUrl":"https://doi.org/10.1090/spmj/1785","url":null,"abstract":"<p>A version of the extra-zero conjecture, formulated by the first named author, is proved for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\"application/x-tex\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-functions associated with Rankin–Selberg convolutions of modular forms of the same weight. This result provides an evidence in support of this conjecture in the <italic>noncritical</italic> case, which remained essentially unstudied.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Triangulated categories of framed bispectra and framed motives","authors":"G. Garkusha, I. Panin","doi":"10.1090/spmj/1786","DOIUrl":"https://doi.org/10.1090/spmj/1786","url":null,"abstract":"<p>An alternative approach to the classical Morel–Voevodsky stable motivic homotopy theory <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S upper H left-parenthesis k right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>H</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>k</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">SH(k)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is suggested. The triangulated category of framed bispectra <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S upper H Subscript n i s Superscript f r Baseline left-parenthesis k right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:msubsup> <mml:mi>H</mml:mi> <mml:mrow> <mml:mi>nis</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>fr</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>k</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">SH_{operatorname {nis}}^{operatorname {fr}}(k)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and effective framed bispectra <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S upper H Subscript n i s Superscript f r comma e f f Baseline left-parenthesis k right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:msubsup> <mml:mi>H</mml:mi> <mml:mrow> <mml:mi>nis</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>fr</mml:mi> <mml:mo>,</mml:mo> <mml:mi>eff</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>k</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">SH_{operatorname {nis}}^{operatorname {fr},operatorname {eff}}(k)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are introduced in the paper. Both triangulated categories only involve Nisnevich local equivalences and have nothing to do with any kind of motivic equivalences. It is shown that <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S upper H Subscript n i s Superscript f r Baseline left-parenthesis k right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:msubsup> <mml:mi>H</mml:mi> <mml:mrow> <mml:mi>nis</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>fr</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>k</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">SH_{operatorname {nis}}^{operatorname {fr}}(k)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S upper H Subscript n i s Superscript f r comma e f f Baseline","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometry of symmetric spaces of type EIII","authors":"V. Petrov, A. Semenov","doi":"10.1090/spmj/1789","DOIUrl":"https://doi.org/10.1090/spmj/1789","url":null,"abstract":"<p>Atsuyama’s result on the geometry of symmetric spaces of type EIII is generalized to the case of arbitrary fields of characteristic not 2 or 3. As an application, a variant of the “chain lemma” for microweight tori in groups of type <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E 6\"> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>6</mml:mn> </mml:msub> <mml:annotation encoding=\"application/x-tex\">E_6</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is proved.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a Blaschke-type condition for the zeros of derivatives of R. Nevanlinna class functions in the disk","authors":"F. Shamoyan","doi":"10.1090/spmj/1790","DOIUrl":"https://doi.org/10.1090/spmj/1790","url":null,"abstract":"<p>A necessary and sufficient Blaschke-type condition is obtained for the zeros of derivatoves of Nevanlinna class functions.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140942116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dubrovin method and the Toda chain","authors":"V. Matveev, A. Smirnov","doi":"10.1090/spmj/1787","DOIUrl":"https://doi.org/10.1090/spmj/1787","url":null,"abstract":"<p>A hierarchy of Lax pairs with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2 times 2\"> <mml:semantics> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>×<!-- × --></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">2times 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> matrix coefficients is presented. The compatibility conditions for these pairs include the Toda chain equation, and other differential-difference integrable systems. Various kinds of finite gap solutions for such systems are constructed. Examples of simplest one- and two-phase solutions are given, together with the corresponding spectral curves.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}