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Chebyshev’s method for exponential maps 切比雪夫的指数映射法
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-19 DOI: 10.1007/s13324-026-01260-0
Subhasis Ghora, Tarakanta Nayak, Soumen Pal, Pooja Phogat
{"title":"Chebyshev’s method for exponential maps","authors":"Subhasis Ghora,&nbsp;Tarakanta Nayak,&nbsp;Soumen Pal,&nbsp;Pooja Phogat","doi":"10.1007/s13324-026-01260-0","DOIUrl":"10.1007/s13324-026-01260-0","url":null,"abstract":"<div><p>It is proved that the Chebyshev’s method applied to an entire function <i>f</i> is a rational map if and only if <span>(f(z) = p(z) e^{q(z)})</span>, for some polynomials <i>p</i> and <i>q</i>. These are referred to as rational Chebyshev maps, and their fixed points are discussed in this article. It is seen that <span>(infty )</span> is a parabolic fixed point with multiplicity one bigger than the degree of <i>q</i>. Considering <span>(q(z)=p(z)^n+c)</span>, where <i>p</i> is a linear polynomial, <span>(n in mathbb {N})</span> and <i>c</i> is a non-zero constant, we show that the Chebyshev’s method applied to <span>( pe^q)</span> is affine conjugate to that applied to <span>(z e^{z^n})</span>. We denote this by <span>(C_n)</span>. All the finite extraneous fixed points of <span>(C_n)</span> are shown to be repelling. The Julia set <span>(mathcal {J}(C_n))</span> of <span>(C_n)</span> is found to be preserved under rotations of order <i>n</i> about the origin. For each <i>n</i>, the immediate basin of 0 is proved to be simply connected. For all <span>(n le 16)</span>, we prove that <span>(mathcal {J}(C_n))</span> is connected. For <i>n</i> even, the non-existence of Herman ring and Siegel disk of <span>(C_n)</span> is proved. Under some additional hypothesis, the same is also proved for odd <i>n</i>. The Newton’s method applied to <span>(ze^{z^n})</span> is found to be conjugate to a polynomial, and its dynamics is also completely determined.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782627","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
From non-polynomial invariants to non-Liouvillian first integrals 从非多项式不变量到非柳维廉第一积分
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-17 DOI: 10.1007/s13324-026-01257-9
Maria Demina, Varvara Nechitailo
{"title":"From non-polynomial invariants to non-Liouvillian first integrals","authors":"Maria Demina,&nbsp;Varvara Nechitailo","doi":"10.1007/s13324-026-01257-9","DOIUrl":"10.1007/s13324-026-01257-9","url":null,"abstract":"<div><p>We present a method of finding non-Liouvillian first integrals of rational two-dimensional differential systems. The method is based on the existence of two independent invariants that satisfy a linear second-order ordinary differential equation with respect to one of the variables. We call systems with this property <i>R</i>-integrable. These invariants are not necessarily polynomial; they can be expressed via special functions. We demonstrate that if there exists a rational transformation that maps some Riccati system to a given rational system, then the latter is always <i>R</i>-integrable. We prove that the famous Van der Pol systems and their generalizations are not <i>R</i>-integrable. We find novel integrable polynomial Liénard differential systems without invariant algebraic curves. The related first integrals are expressible via the Airy functions. We prove that the Kudashev system arising in the theory of the Korteweg–de Vries equation is <i>R</i>-integrable.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782029","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
From non-polynomial invariants to non-Liouvillian first integrals 从非多项式不变量到非柳维廉第一积分
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-17 DOI: 10.1007/s13324-026-01257-9
Maria Demina, Varvara Nechitailo
{"title":"From non-polynomial invariants to non-Liouvillian first integrals","authors":"Maria Demina,&nbsp;Varvara Nechitailo","doi":"10.1007/s13324-026-01257-9","DOIUrl":"10.1007/s13324-026-01257-9","url":null,"abstract":"<div><p>We present a method of finding non-Liouvillian first integrals of rational two-dimensional differential systems. The method is based on the existence of two independent invariants that satisfy a linear second-order ordinary differential equation with respect to one of the variables. We call systems with this property <i>R</i>-integrable. These invariants are not necessarily polynomial; they can be expressed via special functions. We demonstrate that if there exists a rational transformation that maps some Riccati system to a given rational system, then the latter is always <i>R</i>-integrable. We prove that the famous Van der Pol systems and their generalizations are not <i>R</i>-integrable. We find novel integrable polynomial Liénard differential systems without invariant algebraic curves. The related first integrals are expressible via the Airy functions. We prove that the Kudashev system arising in the theory of the Korteweg–de Vries equation is <i>R</i>-integrable.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782023","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 univalent polyharmonic mappings 关于一元多谐映射
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-11 DOI: 10.1007/s13324-026-01255-x
Akash Meher, Priyabrat Gochhayat
{"title":"On univalent polyharmonic mappings","authors":"Akash Meher,&nbsp;Priyabrat Gochhayat","doi":"10.1007/s13324-026-01255-x","DOIUrl":"10.1007/s13324-026-01255-x","url":null,"abstract":"<div><p>In the first part, we study different geometric properties of some well-known families of polyharmonic mappings due to Li et al. (J. Math. Anal. Appl., 434, 1462–1473 [28]). In particular, the sufficient coefficient conditions for the starlikeness and convexity, the conditions on the <span>(q^{th})</span>- integral mean, and the bounds on arclength and Bloch constant of a polyharmonic mapping are obtained. The Bohr phenomenon for harmonic and polyharmonic mappings is studied in the next part. We have refined two results of Kayumov et al. (Math. Nachr., 291(11-12), 1757–1768 [25]) and found their polyharmonic analogue. The article concludes with an improved Bohr phenomenon of <i>K</i>-quasiconformal sense-preserving harmonic mappings.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751736","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 univalent polyharmonic mappings 关于一元多谐映射
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-11 DOI: 10.1007/s13324-026-01255-x
Akash Meher, Priyabrat Gochhayat
{"title":"On univalent polyharmonic mappings","authors":"Akash Meher,&nbsp;Priyabrat Gochhayat","doi":"10.1007/s13324-026-01255-x","DOIUrl":"10.1007/s13324-026-01255-x","url":null,"abstract":"<div><p>In the first part, we study different geometric properties of some well-known families of polyharmonic mappings due to Li et al. (J. Math. Anal. Appl., 434, 1462–1473 [28]). In particular, the sufficient coefficient conditions for the starlikeness and convexity, the conditions on the <span>(q^{th})</span>- integral mean, and the bounds on arclength and Bloch constant of a polyharmonic mapping are obtained. The Bohr phenomenon for harmonic and polyharmonic mappings is studied in the next part. We have refined two results of Kayumov et al. (Math. Nachr., 291(11-12), 1757–1768 [25]) and found their polyharmonic analogue. The article concludes with an improved Bohr phenomenon of <i>K</i>-quasiconformal sense-preserving harmonic mappings.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751733","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
A new generalized fractional musielak-sobolev spaces and its applications 一类新的广义分数型musielak-sobolev空间及其应用
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-10 DOI: 10.1007/s13324-026-01236-0
J. Vanterler da C. Sousa, El-Houari Hamza, Leandro S. Tavares, Arhrrabi Elhoussain
{"title":"A new generalized fractional musielak-sobolev spaces and its applications","authors":"J. Vanterler da C. Sousa,&nbsp;El-Houari Hamza,&nbsp;Leandro S. Tavares,&nbsp;Arhrrabi Elhoussain","doi":"10.1007/s13324-026-01236-0","DOIUrl":"10.1007/s13324-026-01236-0","url":null,"abstract":"<div><p>This paper investigates a novel class of generalized fractional Musielak-Sobolev spaces denoted by <span>(mathcal {H}^{s/2;Psi _{xi ,y}}_{phi })</span>. Key properties such as separability and reflexivity are analyzed in detail. Furthermore, continuous and compact embeddings are rigorously established, together with additional functional-analytic properties. As an application, the framework is used to study the existence and multiplicity of solutions to a class of nonlocal generalized problems, focusing in particular on the nonlocal Schrödinger problem with discontinuous nonlinearity.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01236-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751043","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}
引用次数: 0
A new generalized fractional musielak-sobolev spaces and its applications 一类新的广义分数型musielak-sobolev空间及其应用
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-10 DOI: 10.1007/s13324-026-01236-0
J. Vanterler da C. Sousa, El-Houari Hamza, Leandro S. Tavares, Arhrrabi Elhoussain
{"title":"A new generalized fractional musielak-sobolev spaces and its applications","authors":"J. Vanterler da C. Sousa,&nbsp;El-Houari Hamza,&nbsp;Leandro S. Tavares,&nbsp;Arhrrabi Elhoussain","doi":"10.1007/s13324-026-01236-0","DOIUrl":"10.1007/s13324-026-01236-0","url":null,"abstract":"<div><p>This paper investigates a novel class of generalized fractional Musielak-Sobolev spaces denoted by <span>(mathcal {H}^{s/2;Psi _{xi ,y}}_{phi })</span>. Key properties such as separability and reflexivity are analyzed in detail. Furthermore, continuous and compact embeddings are rigorously established, together with additional functional-analytic properties. As an application, the framework is used to study the existence and multiplicity of solutions to a class of nonlocal generalized problems, focusing in particular on the nonlocal Schrödinger problem with discontinuous nonlinearity.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01236-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751222","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}
引用次数: 0
Extreme points in quotients of Hardy spaces Hardy空间商的极值点
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-08 DOI: 10.1007/s13324-026-01256-w
Konstantin M. Dyakonov
{"title":"Extreme points in quotients of Hardy spaces","authors":"Konstantin M. Dyakonov","doi":"10.1007/s13324-026-01256-w","DOIUrl":"10.1007/s13324-026-01256-w","url":null,"abstract":"<div><p>In the Hardy spaces <span>(H^1)</span> and <span>(H^infty )</span>, there are neat and well-known characterizations of the extreme points of the unit ball. We obtain counterparts of these classical theorems when <span>(H^1)</span> (resp., <span>(H^infty )</span>) gets replaced by the quotient space <span>(H^1/E)</span> (resp., <span>(H^infty /E)</span>), under certain assumptions on the subspace <i>E</i>. In the <span>(H^1)</span> setting, we also treat the case where the underlying space is taken to be the kernel of a Toeplitz operator.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01256-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751013","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}
引用次数: 0
Extreme points in quotients of Hardy spaces Hardy空间商的极值点
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-08 DOI: 10.1007/s13324-026-01256-w
Konstantin M. Dyakonov
{"title":"Extreme points in quotients of Hardy spaces","authors":"Konstantin M. Dyakonov","doi":"10.1007/s13324-026-01256-w","DOIUrl":"10.1007/s13324-026-01256-w","url":null,"abstract":"<div><p>In the Hardy spaces <span>(H^1)</span> and <span>(H^infty )</span>, there are neat and well-known characterizations of the extreme points of the unit ball. We obtain counterparts of these classical theorems when <span>(H^1)</span> (resp., <span>(H^infty )</span>) gets replaced by the quotient space <span>(H^1/E)</span> (resp., <span>(H^infty /E)</span>), under certain assumptions on the subspace <i>E</i>. In the <span>(H^1)</span> setting, we also treat the case where the underlying space is taken to be the kernel of a Toeplitz operator.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01256-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751012","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}
引用次数: 0
Quasiperiodic inverse Sturm-Liouville problem 拟周期逆Sturm-Liouville问题
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-05 DOI: 10.1007/s13324-026-01253-z
Natalia P. Bondarenko
{"title":"Quasiperiodic inverse Sturm-Liouville problem","authors":"Natalia P. Bondarenko","doi":"10.1007/s13324-026-01253-z","DOIUrl":"10.1007/s13324-026-01253-z","url":null,"abstract":"<div><p>In this paper, the Sturm-Liouville problem with nonseparated quasiperiodic boundary conditions is considered. We study the recovery of the problem parameters from the Hill-type discriminant, the Dirichlet spectrum, and the sequence of signs. We obtain the necessary and sufficient conditions of solvability, the local solvability and stability, as well as the uniform stability for this inverse spectral problem.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750879","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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