Mathematische Nachrichten最新文献

{"title":"On some properties of generalized squeezing functions and Fridman invariants","authors":"Shichao Yang,&nbsp;Shuo Zhang","doi":"10.1002/mana.202300268","DOIUrl":"10.1002/mana.202300268","url":null,"abstract":"<p>The purpose of this paper is twofold. The first aim is to study the comparison of generalized squeezing functions and Fridaman invariants of some special domains. Then, the second aim is to give estimates for these two invariants and discuss their boundary behavior near inessential boundary points.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140594298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On noncompact warped product Ricci solitons","authors":"V. Borges","doi":"10.1002/mana.202300312","DOIUrl":"10.1002/mana.202300312","url":null,"abstract":"<p>The goal of this paper is to investigate complete noncompact warped product gradient Ricci solitons. Nonexistence results, estimates for the warping function and for its gradient are proven. When the soliton is steady or expanding these nonexistence results generalize to a broader context certain  estimates and rigidity obtained when studying warped product Einstein manifolds. When the soliton is shrinking, it is presented as a nonexistence theorem with no counterpart in the Einstein case, which is proved using properties of the first eigenvalue of a weighted Laplacian.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140594304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The boundedness of operators on weighted multi-parameter mixed Hardy spaces","authors":"Wei Ding,&nbsp;Min Gu,&nbsp;YuePing Zhu","doi":"10.1002/mana.202300291","DOIUrl":"10.1002/mana.202300291","url":null,"abstract":"<p>In this paper, we discuss the boundedness of mixed Journé's class operators on weighted multi-parameter mixed Hardy spaces via atoms decomposition. Moreover, we give a specific singular integral operator in mixed Journé's class which has better properties.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140594231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Endpoint estimates for harmonic analysis operators associated with Laguerre polynomial expansions","authors":"Jorge J. Betancor,&nbsp;Estefanía Dalmasso,&nbsp;Pablo Quijano,&nbsp;Roberto Scotto","doi":"10.1002/mana.202300088","DOIUrl":"10.1002/mana.202300088","url":null,"abstract":"<p>In this paper, we give a criterion to prove boundedness results for several operators from the Hardy-type space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>γ</mi>\u0000 <mi>α</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$H^1((0,infty)^d,gamma _alpha)$</annotation>\u0000 </semantics></math> to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>γ</mi>\u0000 <mi>α</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L^1((0,infty)^d,gamma _alpha)$</annotation>\u0000 </semantics></math> and also from <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>γ</mi>\u0000 <mi>α</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L^infty ((0,infty)^d,gamma _alpha)$</annotation>\u0000 </semantics></math> to the space of functions of bounded mean oscillation <span></span><math>\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140323080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Kirchhoff-type critical fractional Laplacian system with convolution and magnetic field","authors":"Sihua Liang,&nbsp;Binlin Zhang","doi":"10.1002/mana.202200172","DOIUrl":"10.1002/mana.202200172","url":null,"abstract":"<p>In this paper, we consider a class of upper critical Kirchhoff-type fractional Laplacian system with Choquard nonlinearities and magnetic fields. With the help of the limit index theory and the concentration–compactness principles for fractional Sobolev spaces, we establish the existence of infinitely many nontrivial radial solutions for the above system. A distinguished feature of this paper is that the above Kirchhoff-type system is degenerate, that is, the Kirchhoff term is zero at zero.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140322881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a class of doubly nonlinear evolution equations in Musielak–Orlicz spaces","authors":"Goro Akagi,&nbsp;Giulio Schimperna","doi":"10.1002/mana.202300374","DOIUrl":"10.1002/mana.202300374","url":null,"abstract":"<p>This paper is concerned with a parabolic evolution equation of the form <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>u</mi>\u0000 <mi>t</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>+</mo>\u0000 <mi>B</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>u</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>=</mo>\u0000 <mi>f</mi>\u0000 </mrow>\u0000 <annotation>$A(u_t) + B(u) = f$</annotation>\u0000 </semantics></math>, settled in a smooth bounded domain of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^d$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>≥</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$dge 1$</annotation>\u0000 </semantics></math>, and complemented with the initial conditions and with (for simplicity) homogeneous Dirichlet boundary conditions. Here, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mi>B</mi>\u0000 </mrow>\u0000 <annotation>$-B$</annotation>\u0000 </semantics></math> stands for a diffusion operator, possibly nonlinear, which may range in a very wide class, including the Laplacian, the <span></span><math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math>-Laplacian for suitable <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$min (1,infty)$</annotation>\u0000 </semantics></math>, the “variable-exponent” <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$m(x)$</annotation>\u0000 </semantics></math>-Laplacian, or even some fractional order operators. The operator <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> is assumed to be in the form <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mi>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140303081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The \u0000 \u0000 \u0000 W\u0000 (\u0000 \u0000 E\u0000 6\u0000 \u0000 )\u0000 \u0000 $W(E_6)$\u0000 -invariant birational geometry of the moduli space of marked cubic surfaces","authors":"Nolan Schock","doi":"10.1002/mana.202300459","DOIUrl":"10.1002/mana.202300459","url":null,"abstract":"<p>The moduli space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Y</mi>\u0000 <mo>=</mo>\u0000 <mi>Y</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>6</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Y = Y(E_6)$</annotation>\u0000 </semantics></math> of marked cubic surfaces is one of the most classical moduli spaces in algebraic geometry, dating back to the nineteenth-century work of Cayley and Salmon. Modern interest in <span></span><math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$Y$</annotation>\u0000 </semantics></math> was restored in the 1980s by Naruki's explicit construction of a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>W</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>6</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$W(E_6)$</annotation>\u0000 </semantics></math>-equivariant smooth projective compactification <span></span><math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>Y</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <annotation>${overline{Y}}$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$Y$</annotation>\u0000 </semantics></math>, and in the 2000s by Hacking, Keel, and Tevelev's construction of the Kollár–Shepherd-Barron–Alexeev (KSBA) stable pair compactification <span></span><math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>Y</mi>\u0000 <mo>∼</mo>\u0000 </mover>\u0000 <annotation>${widetilde{Y}}$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$Y$</annotation>\u0000 </semantics></math> as a natural sequence of blowups of <span></span><math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>Y</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <annotation>${overline{Y}}$</annotation>\u0000 </semantics></math>. We describe generators for the cones of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>W</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>6</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300459","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uniform bounds of families of analytic semigroups and Lyapunov Linear Stability of planar fronts","authors":"Yuri Latushkin,&nbsp;Alin Pogan","doi":"10.1002/mana.202300273","DOIUrl":"10.1002/mana.202300273","url":null,"abstract":"<p>We study families of analytic semigroups, acting on a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parameter norm bounds using spectral properties of the respective semigroup generators. In particular, we use estimates of the resolvent operators of the generators along vertical segments to estimate the growth/decay rate of the norm for the family of analytic semigroups. These results are applied to prove the Lyapunov linear stability of planar traveling waves of systems of reaction–diffusion equations, and the bidomain equation, important in electrophysiology.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Equivariant \u0000 \u0000 K\u0000 $K$\u0000 -theory of flag Bott manifolds of general Lie type","authors":"Bidhan Paul,&nbsp;Vikraman Uma","doi":"10.1002/mana.202300423","DOIUrl":"10.1002/mana.202300423","url":null,"abstract":"<p>The aim of this paper is to describe the equivariant and ordinary Grothendieck ring and the equivariant and ordinary topological <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-ring of flag Bott manifolds of the general Lie type. This will generalize the results on the equivariant and ordinary cohomology of flag Bott manifolds of the general Lie type due to Kaji, Kuroki, Lee, and Suh.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Second-order trace formulas","authors":"Arup Chattopadhyay,&nbsp;Soma Das,&nbsp;Chandan Pradhan","doi":"10.1002/mana.202200295","DOIUrl":"10.1002/mana.202200295","url":null,"abstract":"<p>Koplienko [Sib. Mat. Zh. 25 (1984), 62–71; English transl. in Siberian Math. J. 25 (1984), 735–743] found a trace formula for perturbations of self-adjoint operators by operators of Hilbert–Schmidt class <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>H</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathcal {B}_2(mathcal {H})$</annotation>\u0000 </semantics></math>. Later, Neidhardt introduced a similar formula in the case of pairs of unitaries <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>U</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>U</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(U,U_0)$</annotation>\u0000 </semantics></math> via multiplicative path in [Math. Nachr. 138 (1988), 7–25]. In 2012, Potapov and Sukochev [Comm. Math. Phys. 309 (2012), no. 3, 693–702] obtained a trace formula like the Koplienko trace formula for pairs of contractions by answering an open question posed by Gesztesy, Pushnitski, and Simon [Zh. Mat. Fiz. Anal. Geom. 4 (2008), no. 1, 63–107, 202; Open Question 11.2]. In this paper, we supply a new proof of the Koplienko trace formula in the case of pairs of contractions <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>T</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>T</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(T,T_0)$</annotation>\u0000 </semantics></math>, where the initial operator <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>T</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$T_0$</annotation>\u0000 </semantics></math> is normal, via linear path by reducing the problem to a finite-dimensional one as in the proof of Krein's trace formula by Voiculescu [Oper. Theory Adv. Appl. 24 (1987) 329–332] and Sinha and Mohapatra [Proc. Indian Acad. Sci. Math. Sci. 104 (1994), no. 4, 819–853] and [Integral Equations Operator Theory 24 (1996), no. 3, 285–297]. Consequently, we obtain the Koplienko trace formula for a class of pairs of contractions using the Schäffer matrix unitary dilation. Moreover, we also obtain the Koplienko trace formula for a pair of self-adjoint operators and maximal dissipative operators using the Cayley transform. At the end, we extend the Koplienko–Neidhardt trace formula for a class of pairs of contractions <span></span","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}