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Balayage, equilibrium measure, and Deny’s principle of positivity of mass for (alpha )-Green potentials 平衡测量，以及(alpha ) -格林势的质量正性的否定原理
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-12-13 DOI: 10.1007/s13324-024-00995-y
Natalia Zorii
{"title":"Balayage, equilibrium measure, and Deny’s principle of positivity of mass for (alpha )-Green potentials","authors":"Natalia Zorii","doi":"10.1007/s13324-024-00995-y","DOIUrl":"10.1007/s13324-024-00995-y","url":null,"abstract":"<div><p>In the theory of <span>(g_alpha )</span>-potentials on a domain <span>(Dsubset mathbb R^n)</span>, <span>(ngeqslant 2)</span>, <span>(g_alpha )</span> being the <span>(alpha )</span>-Green kernel associated with the <span>(alpha )</span>-Riesz kernel <span>(|x-y|^{alpha -n})</span> of order <span>(alpha in (0,n))</span>, <span>(alpha leqslant 2)</span>, we establish the existence and uniqueness of the <span>(g_alpha )</span>-balayage <span>(mu ^F)</span> of a positive Radon measure <span>(mu )</span> onto a relatively closed set <span>(Fsubset D)</span>, we analyze its alternative characterizations, and we provide necessary and/or sufficient conditions for <span>(mu ^F(D)=mu (D))</span> to hold, given in terms of the <span>(alpha )</span>-harmonic measure of suitable Borel subsets of <span>(overline{mathbb R^n})</span>, the one-point compactification of <span>(mathbb R^n)</span>. As a by-product, we find necessary and/or sufficient conditions for the existence of the <span>(g_alpha )</span>-equilibrium measure <span>(gamma _F)</span>, <span>(gamma _F)</span> being understood in an extended sense where <span>(gamma _F(D))</span> might be infinite. We also discover quite a surprising version of Deny’s principle of positivity of mass for <span>(g_alpha )</span>-potentials, thereby significantly improving a previous result by Fuglede and Zorii (Ann Acad Sci Fenn Math 43:121–145, 2018). The results thus obtained are sharp, which is illustrated by means of a number of examples. Some open questions are also posed.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142810994","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
Old and new on the Peetre K-functional and its relations to real interpolation theory, quasi-monotone functions and wavelets 彼得k泛函的新与旧及其与实插值理论、拟单调函数和小波的关系
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-12-10 DOI: 10.1007/s13324-024-00998-9
Rune Dalmo, Lars-Erik Persson, Natasha Samko
{"title":"Old and new on the Peetre K-functional and its relations to real interpolation theory, quasi-monotone functions and wavelets","authors":"Rune Dalmo,&nbsp;Lars-Erik Persson,&nbsp;Natasha Samko","doi":"10.1007/s13324-024-00998-9","DOIUrl":"10.1007/s13324-024-00998-9","url":null,"abstract":"<div><p>The Peetre K-functional is a key object in the development of the real method of interpolation. In this paper we point out a less known relation to wavelet theory and its applications to approximation theory and engineering applications. As a new basis for further development of these studies we present some known properties in the form appropriate for further applications and then derive new information and prove some new results concerning the K-functional and its close relation to (almost) quasi-monotone functions, various indices and interpolation theory. In particular, we extend and unify some known function parameter generalizations of the standard real interpolation spaces <span>((A_0, A_1)_{theta ,q})</span>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00998-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142798257","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
Questions in linear recurrence I: the (Toplus T)-recurrence problem 线性递归中的问题1:(Toplus T)递归问题
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-12-09 DOI: 10.1007/s13324-024-00999-8
Sophie Grivaux, Antoni López-Martínez, Alfred Peris
{"title":"Questions in linear recurrence I: the (Toplus T)-recurrence problem","authors":"Sophie Grivaux,&nbsp;Antoni López-Martínez,&nbsp;Alfred Peris","doi":"10.1007/s13324-024-00999-8","DOIUrl":"10.1007/s13324-024-00999-8","url":null,"abstract":"<div><p>We study, for a continuous linear operator <i>T</i> acting on an F-space <i>X</i>, when the direct sum operator <span>(Toplus T)</span> is recurrent on the direct sum space <span>(Xoplus X)</span>. In particular: we establish the analogous notion for recurrence to that of (topological) weak-mixing for transitivity/hypercyclicity, namely quasi-rigidity; and we construct a recurrent but not quasi-rigid operator on each separable infinite-dimensional Banach space, solving the <span>(Toplus T)</span>-recurrence problem in the negative way.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00999-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142798436","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
Symmetrization process and truncated orthogonal polynomials 对称过程与截断正交多项式
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-29 DOI: 10.1007/s13324-024-00974-3
Diego Dominici, Juan Carlos García-Ardila, Francisco Marcellán
{"title":"Symmetrization process and truncated orthogonal polynomials","authors":"Diego Dominici,&nbsp;Juan Carlos García-Ardila,&nbsp;Francisco Marcellán","doi":"10.1007/s13324-024-00974-3","DOIUrl":"10.1007/s13324-024-00974-3","url":null,"abstract":"<div><p>We define the family of truncated Laguerre polynomials <span>(P_n(x;z))</span>, orthogonal with respect to the linear functional <span>(varvec{ell })</span> defined by </p><div><div><span>$$begin{aligned} leftlangle {varvec{ell },p}rightrangle =int _{0}^zp(x)x^alpha e^{-x}dx,qquad alpha &gt;-1. end{aligned}$$</span></div></div><p>The connection between <span>(P_n(x;z))</span> and the polynomials <span>(S_n(x;z))</span> (obtained through the symmetrization process) constitutes a key element in our analysis. As a consequence, several properties of the polynomials <span>(P_n(x;z))</span> and <span>(S_n(x;z))</span> are studied taking into account the relation between the parameters of the three-term recurrence relations that they satisfy. Asymptotic expansions of these coefficients are given. Discrete Painlevé and Painlevé equations associated with such coefficients appear in a natural way. An electrostatic interpretation of the zeros of such polynomials as well as the dynamics of the zeros in terms of the parameter <i>z</i> are given.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00974-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142754025","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
The analytic content is not semiadditive 分析内容不具有半加性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-28 DOI: 10.1007/s13324-024-00994-z
Eduardo S. Zeron, Paul M. Gauthier
{"title":"The analytic content is not semiadditive","authors":"Eduardo S. Zeron,&nbsp;Paul M. Gauthier","doi":"10.1007/s13324-024-00994-z","DOIUrl":"10.1007/s13324-024-00994-z","url":null,"abstract":"<div><p>We show that the analytic content <span>(lambda (cdot ))</span> is neither subadditive nor semiadditive. To be precise, for compact sets <i>K</i> in the complex plane, <span>(lambda (K))</span> is the <i>K</i>-uniform distance from the complex conjugation to the algebra of all rational functions with poles outside <i>K</i>. Thus, given any integer <span>(nge 1)</span>, it is proven that each compactum <i>K</i> can be decomposed as the union of two new compact sets <span>(E_1)</span> and <span>(E_2)</span> with <span>(lambda (E_j)le 1/n)</span> for <span>(j=1,2)</span>. Moreover, we also show that no compactum <i>K</i> with positive analytic content can be decomposed as the countable union of compact sets of zero analytic content.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00994-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737227","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
Functional model for generalised resolvents and its application to time-dispersive media 广义解析子的函数模型及其在时间色散介质中的应用
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-28 DOI: 10.1007/s13324-024-00993-0
Kirill D. Cherednichenko, Yulia Yu. Ershova, Sergey N. Naboko
{"title":"Functional model for generalised resolvents and its application to time-dispersive media","authors":"Kirill D. Cherednichenko,&nbsp;Yulia Yu. Ershova,&nbsp;Sergey N. Naboko","doi":"10.1007/s13324-024-00993-0","DOIUrl":"10.1007/s13324-024-00993-0","url":null,"abstract":"<div><p>Motivated by recent results concerning the asymptotic behaviour of differential operators with highly contrasting coefficients, whose effective descriptions have involved generalised resolvents, we construct the functional model for a typical example of the latter. This provides a spectral representation for the generalised resolvent, which can be utilised for further analysis, in particular the construction of the scattering operator in related wave propagation setups.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00993-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737226","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
Correction: On entire solutions of certain partial differential equations 更正：关于某些偏微分方程的全解
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-27 DOI: 10.1007/s13324-024-00997-w
Feng Lü, Wenqi Bi
{"title":"Correction: On entire solutions of certain partial differential equations","authors":"Feng Lü,&nbsp;Wenqi Bi","doi":"10.1007/s13324-024-00997-w","DOIUrl":"10.1007/s13324-024-00997-w","url":null,"abstract":"","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714225","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: Preimages under linear combinations of iterates of finite Blaschke products 更正：有限布拉什克积迭代的线性组合下的预成像
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1007/s13324-024-00996-x
Spyridon Kakaroumpas, Odí Soler i Gibert
{"title":"Correction: Preimages under linear combinations of iterates of finite Blaschke products","authors":"Spyridon Kakaroumpas,&nbsp;Odí Soler i Gibert","doi":"10.1007/s13324-024-00996-x","DOIUrl":"10.1007/s13324-024-00996-x","url":null,"abstract":"","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00996-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714255","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
Symmetries of large BKP hierarchy 大型 BKP 层次结构的对称性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-20 DOI: 10.1007/s13324-024-00992-1
Wenchuang Guan, Shen Wang, Jipeng Cheng
{"title":"Symmetries of large BKP hierarchy","authors":"Wenchuang Guan,&nbsp;Shen Wang,&nbsp;Jipeng Cheng","doi":"10.1007/s13324-024-00992-1","DOIUrl":"10.1007/s13324-024-00992-1","url":null,"abstract":"<div><p>Symmetries of the large BKP hierarchy, also known as Toda hierarchy of B type, are investigated in this paper. We firstly construct symmetries of the large BKP hierarchy by the method of additional symmetries. Then we derive Adler–Shiota–van Morebeke formula to link the actions of additional symmetries on Lax operators and tau functions.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679514","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
Lieb–Thirring inequalities on the spheres and SO(3) 球面和 SO(3) 上的李卜-蒂林不等式
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-19 DOI: 10.1007/s13324-024-00991-2
André Kowacs, Michael Ruzhansky
{"title":"Lieb–Thirring inequalities on the spheres and SO(3)","authors":"André Kowacs,&nbsp;Michael Ruzhansky","doi":"10.1007/s13324-024-00991-2","DOIUrl":"10.1007/s13324-024-00991-2","url":null,"abstract":"<div><p>In this paper, we obtain new upper bounds for the Lieb–Thirring inequality on the spheres of any dimension greater than 2. As far as we have checked, our results improve previous results found in the literature for all dimensions greater than 2. We also prove and exhibit an explicit new upper bound for the Lieb–Thirring inequality on <i>SO</i>(3). We also discuss these estimates in the case of general compact Lie groups. Originally developed for estimating the sums of moments of negative eigenvalues of the Schrödinger operator in <span>(L^2(mathbb {R}^n))</span>, these inequalities have applications in quantum mechanics and other fields.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672479","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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