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Toeplitz operators and Hankel operators on a Bergman space with an exponential weight on the unit ball 单位球上具有指数权重的伯格曼空间上的托普利兹算子和汉克尔算子
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-07-16 DOI: 10.1007/s13324-024-00947-6
Hong Rae Cho, Han-Wool Lee, Soohyun Park
{"title":"Toeplitz operators and Hankel operators on a Bergman space with an exponential weight on the unit ball","authors":"Hong Rae Cho,&nbsp;Han-Wool Lee,&nbsp;Soohyun Park","doi":"10.1007/s13324-024-00947-6","DOIUrl":"10.1007/s13324-024-00947-6","url":null,"abstract":"<div><p>We consider the weighted Bergman space <span>(A^2_psi )</span> of all holomorphic functions on <span>({textbf{B}_n})</span> square integrable with respect to an exponential weight measure <span>(e^{-{psi }} dV)</span> on <span>({textbf{B}_n})</span>, where </p><div><div><span>$$begin{aligned} psi (z):=frac{1}{1-|z|^2}. end{aligned}$$</span></div></div><p>We characterize boundedness (or compactness) of Toeplitz operators and Hankel operators on <span>(A^2_psi )</span>.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141641877","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}
引用次数: 0
Positive solutions of Kirchhoff type problems with critical growth on exterior domains 外部域上具有临界增长的基尔霍夫类型问题的正解
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-07-11 DOI: 10.1007/s13324-024-00944-9
Ting-Ting Dai, Zeng-Qi Ou, Chun-Lei Tang, Ying Lv
{"title":"Positive solutions of Kirchhoff type problems with critical growth on exterior domains","authors":"Ting-Ting Dai,&nbsp;Zeng-Qi Ou,&nbsp;Chun-Lei Tang,&nbsp;Ying Lv","doi":"10.1007/s13324-024-00944-9","DOIUrl":"10.1007/s13324-024-00944-9","url":null,"abstract":"<div><p>In this paper, we study the existence of positive solutions for a class of Kirchhoff equation with critical growth </p><div><div><span>$$begin{aligned} left{ begin{aligned}&amp;-left( a+b int _{Omega }|nabla u|^{2} d xright) Delta u+V(x) u=u^{5}&amp;text{ in } Omega , &amp;uin D^{1,2}_0(Omega ), end{aligned}right. end{aligned}$$</span></div></div><p>where <span>(a&gt;0)</span>, <span>(b&gt;0)</span>, <span>(Vin L^frac{3}{2}(Omega ))</span> is a given nonnegative function and <span>(Omega subseteq mathbb {R}^3)</span> is an exterior domain, that is, an unbounded domain with smooth boundary <span>(partial Omega ne emptyset )</span> such that <span>(mathbb {R}^3backslash Omega )</span> non-empty and bounded. By using barycentric functions and Brouwer degree theory to prove that there exists a positive solution <span>(uin D^{1,2}_0(Omega ))</span> if <span>(mathbb {R}^3backslash Omega )</span> is contained in a small ball.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141585083","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}
引用次数: 0
Generalized Hölder estimates via generalized Morrey norms for some ultraparabolic operators 通过一些超抛物线算子的广义莫雷规范实现广义荷尔德估计
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-07-10 DOI: 10.1007/s13324-024-00941-y
V. S. Guliyev
{"title":"Generalized Hölder estimates via generalized Morrey norms for some ultraparabolic operators","authors":"V. S. Guliyev","doi":"10.1007/s13324-024-00941-y","DOIUrl":"10.1007/s13324-024-00941-y","url":null,"abstract":"<div><p>We consider a class of hypoelliptic operators of the following type </p><div><div><span>$$begin{aligned} {mathcal {L}}=sum limits _{i,j=1}^{p_0} a_{ij} partial _{x_i x_j}^2+sum limits _{i,j=1}^{N} b_{ij} x_i partial _{x_j}-partial _t, end{aligned}$$</span></div></div><p>where <span>((a_{ij}))</span>, <span>((b_{ij}))</span> are constant matrices and <span>((a_{ij}))</span> is symmetric positive definite on <span>({mathbb {R}}^{p_0})</span> <span>((p_0le N))</span>. We obtain generalized Hölder estimates for <span>({mathcal {L}})</span> on <span>({mathbb {R}}^{N+1})</span> by establishing several estimates of singular integrals in generalized Morrey spaces.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574839","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}
引用次数: 0
Weighted holomorphic polynomial approximation 加权全形多项式近似法
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-07-08 DOI: 10.1007/s13324-024-00943-w
S. Charpentier, N. Levenberg, F. Wielonsky
{"title":"Weighted holomorphic polynomial approximation","authors":"S. Charpentier,&nbsp;N. Levenberg,&nbsp;F. Wielonsky","doi":"10.1007/s13324-024-00943-w","DOIUrl":"10.1007/s13324-024-00943-w","url":null,"abstract":"<div><p>For <i>G</i> an open set in <span>({mathbb {C}})</span> and <i>W</i> a non-vanishing holomorphic function in <i>G</i>, in the late 1990’s, Pritsker and Varga (Constr Approx 14, 475-492 1998) characterized pairs (<i>G</i>, <i>W</i>) having the property that any <i>f</i> holomorphic in <i>G</i> can be locally uniformly approximated in <i>G</i> by weighted holomorphic polynomials <span>({W(z)^np_n(z)}, deg(p_n)le n)</span>. We further develop their theory in first proving a quantitative Bernstein-Walsh type theorem for certain pairs (<i>G</i>, <i>W</i>). Then we consider the special case where <span>(W(z)=1/(1+z))</span> and <i>G</i> is a loop of the lemniscate <span>({zin {mathbb {C}}: |z(z+1)|=1/4})</span>. We show the normalized measures associated to the zeros of the <span>(n-th)</span> order Taylor polynomial about 0 of the function <span>((1+z)^{-n})</span> converge to the weighted equilibrium measure of <span>({overline{G}})</span> with weight |<i>W</i>| as <span>(nrightarrow infty )</span>. This mimics the motivational case of Pritsker and Varga (Trans Amer Math Soc 349, 4085-4105 1997) where <i>G</i> is the inside of the Szegő curve and <span>(W(z)=e^{-z})</span>. Lastly, we initiate a study of weighted holomorphic polynomial approximation in <span>({mathbb {C}}^n, n&gt;1)</span>.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574840","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}
引用次数: 0
Convergence of generalized MIT bag models to Dirac operators with zigzag boundary conditions 广义 MIT 袋模型收敛于具有之字形边界条件的狄拉克算子
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-07-08 DOI: 10.1007/s13324-024-00946-7
Joaquim Duran, Albert Mas
{"title":"Convergence of generalized MIT bag models to Dirac operators with zigzag boundary conditions","authors":"Joaquim Duran,&nbsp;Albert Mas","doi":"10.1007/s13324-024-00946-7","DOIUrl":"10.1007/s13324-024-00946-7","url":null,"abstract":"<div><p>This work addresses the resolvent convergence of generalized MIT bag operators to Dirac operators with zigzag type boundary conditions. We prove that the convergence holds in strong but not in norm resolvent sense. Moreover, we show that the only obstruction for having norm resolvent convergence is the existence of an eigenvalue of infinite multiplicity for the limiting operator. More precisely, we prove the convergence of the resolvents in operator norm once projected into the orthogonal of the corresponding eigenspace.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574841","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}
引用次数: 0
Uniform-in-mass global existence for 4D Dirac–Klein–Gordon equations 四维狄拉克-克莱因-戈登方程的均匀质量全局存在性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-07-06 DOI: 10.1007/s13324-024-00945-8
Jingya Zhao
{"title":"Uniform-in-mass global existence for 4D Dirac–Klein–Gordon equations","authors":"Jingya Zhao","doi":"10.1007/s13324-024-00945-8","DOIUrl":"10.1007/s13324-024-00945-8","url":null,"abstract":"<div><p>We are interested in four-dimensional Dirac–Klein–Gordon equations, a fundamental model in particle physics. The main goal of this paper is to establish global existence of solutions to the coupled system and to explore their long-time behavior. The results are valid uniformly for mass parameters varying in the interval [0, 1].</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574869","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}
引用次数: 0
Lie reductions and exact solutions of dispersionless Nizhnik equation 无分散尼兹尼克方程的列还原和精确解
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-07-05 DOI: 10.1007/s13324-024-00925-y
Oleksandra O. Vinnichenko, Vyacheslav M. Boyko, Roman O. Popovych
{"title":"Lie reductions and exact solutions of dispersionless Nizhnik equation","authors":"Oleksandra O. Vinnichenko,&nbsp;Vyacheslav M. Boyko,&nbsp;Roman O. Popovych","doi":"10.1007/s13324-024-00925-y","DOIUrl":"10.1007/s13324-024-00925-y","url":null,"abstract":"<div><p>We exhaustively classify the Lie reductions of the real dispersionless Nizhnik equation to partial differential equations in two independent variables and to ordinary differential equations. Lie and point symmetries of reduced equations are comprehensively studied, including the analysis of which of them correspond to hidden symmetries of the original equation. If necessary, associated Lie reductions of a nonlinear Lax representation of the dispersionless Nizhnik equation are carried out as well. As a result, we construct wide families of new invariant solutions of this equation in explicit form in terms of elementary, Lambert and hypergeometric functions as well as in parametric or implicit form. We show that Lie reductions to algebraic equations lead to no new solutions of this equation in addition to the constructed ones. Multiplicative separation of variables is used for illustrative construction of non-invariant solutions.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547903","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}
引用次数: 0
On the regular representation of solvable Lie groups with open coadjoint quasi-orbits 论具有开放共轭准邻域的可解列群的正则表达式
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-07-04 DOI: 10.1007/s13324-024-00942-x
Ingrid Beltiţă, Daniel Beltiţă
{"title":"On the regular representation of solvable Lie groups with open coadjoint quasi-orbits","authors":"Ingrid Beltiţă,&nbsp;Daniel Beltiţă","doi":"10.1007/s13324-024-00942-x","DOIUrl":"10.1007/s13324-024-00942-x","url":null,"abstract":"<div><p>We obtain a Lie theoretic intrinsic characterization of the connected and simply connected solvable Lie groups whose regular representation is a factor representation. When this is the case, the corresponding von Neumann algebras are isomorphic to the hyperfinite <span>(textrm{II}_infty )</span> factor, and every Casimir function is constant. We thus obtain a family of geometric models for the standard representation of that factor. Finally, we show that the regular representation of any connected and simply connected solvable Lie group with open coadjoint orbits is always of type <span>(textrm{I})</span>, though the group needs not be of type <span>(textrm{I})</span>, and include some relevant examples.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547905","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}
引用次数: 0
Correction: On solutions of two categories of q-shift equations in two dimensional complex field 更正：关于二维复数场中两类 q 移位方程的解
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-06-26 DOI: 10.1007/s13324-024-00939-6
Abhijit Banerjee, Jhuma Sarkar
{"title":"Correction: On solutions of two categories of q-shift equations in two dimensional complex field","authors":"Abhijit Banerjee,&nbsp;Jhuma Sarkar","doi":"10.1007/s13324-024-00939-6","DOIUrl":"10.1007/s13324-024-00939-6","url":null,"abstract":"","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414083","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}
引用次数: 0
Ground state solitons for periodic Schrödinger lattice systems with saturable nonlinearities and spectrum 0 具有可饱和非线性和频谱 0 的周期性薛定谔晶格系统的基态孤子
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-06-20 DOI: 10.1007/s13324-024-00936-9
Guanwei Chen, Shiwang Ma
{"title":"Ground state solitons for periodic Schrödinger lattice systems with saturable nonlinearities and spectrum 0","authors":"Guanwei Chen,&nbsp;Shiwang Ma","doi":"10.1007/s13324-024-00936-9","DOIUrl":"10.1007/s13324-024-00936-9","url":null,"abstract":"<div><p>This paper is concerned with a class of periodic Schrödinger lattice systems with spectrum 0 and saturable nonlinearities. The existence of ground state solitons of the systems under weak assumptions is obtained. The main novelties are as follows. (1) Some new sufficient conditions for the existence of ground state solitons under the “spectral endpoint” assumption are constructed. (2) Our “non-monotonic” conditions make the proofs of the boundedness of the (<i>PS</i>) sequences to be easier. (3) Our result extends and improves the related results in the literature. Besides, some examples are given to illuminate our result.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506714","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}
引用次数: 0
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