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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
Meromorphic solutions of Bi-Fermat type partial differential and difference equations 比-费马型偏微分方程和差分方程的同态解
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-16 DOI: 10.1007/s13324-024-00989-w
Yingchun Gao, Kai Liu
{"title":"Meromorphic solutions of Bi-Fermat type partial differential and difference equations","authors":"Yingchun Gao,&nbsp;Kai Liu","doi":"10.1007/s13324-024-00989-w","DOIUrl":"10.1007/s13324-024-00989-w","url":null,"abstract":"<div><p>Fermat type functional equation with four terms </p><div><div><span>$$begin{aligned} f(z)^{n}+g(z)^{n}+h(z)^{n}+k(z)^{n}=1 end{aligned}$$</span></div></div><p>is difficult to solve completely even if <span>(n=2,3)</span>, in which the certain type of the above equation is also interesting and significant. In this paper, we first to consider the Bi-Fermat type quadratic partial differential equation </p><div><div><span>$$begin{aligned} f(z_{1},z_{2})^{2}+left( frac{partial f(z_{1},z_{2})}{partial z_{1}}right) ^{2}+g(z_{1},z_{2})^{2}+left( frac{partial g(z_{1},z_{2})}{partial z_{1}}right) ^{2}=1 end{aligned}$$</span></div></div><p>in <span>(mathbb {C}^{2})</span>. In addition, we consider the Bi-Fermat type cubic difference equation </p><div><div><span>$$begin{aligned} f(z)^{3}+g(z)^{3}+f(z+c)^{3}+g(z+c)^{3}=1 end{aligned}$$</span></div></div><p>in <span>(mathbb {C})</span> and obtain partial meromorphic solutions on the above equation.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645697","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
Value distribution of meromorphic functions concerning differences 关于差分的分形函数的值分布
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-16 DOI: 10.1007/s13324-024-00990-3
Zhiying He, Ge Wang, Mingliang Fang
{"title":"Value distribution of meromorphic functions concerning differences","authors":"Zhiying He,&nbsp;Ge Wang,&nbsp;Mingliang Fang","doi":"10.1007/s13324-024-00990-3","DOIUrl":"10.1007/s13324-024-00990-3","url":null,"abstract":"<div><p>In this paper, we study value distribution of meromorphic functions concerning differences and mainly prove the following result: Let <i>f</i> be a transcendental meromorphic function of <span>(1 le rho (f) &lt; infty )</span>, let <i>c</i> be a nonzero constant, <i>n</i> a positive integer, and let <i>P</i>, <i>Q</i> be two polynomials. If <span>(max left{ lambda (f-P), lambda left( frac{1}{f}right) right} &lt;rho (f))</span> and <span>(Delta _{c}^{n}f not equiv 0)</span>, then we have (i) <span>(delta (Q, Delta _c^n f)=0)</span> and <span>(lambda (Delta _{c}^{n}f-Q)=rho (f))</span>, for <span>(Delta _{c}^{n}Pnot equiv Q)</span>; (ii) <span>(delta (Q, Delta _c^n f)=1)</span> and <span>(lambda (Delta _{c}^{n}f-Q)&lt;rho (f))</span>, for <span>(Delta _{c}^{n}Pequiv Q)</span>. The results obtained in this paper extend and improve some results due to Chen-Shon[J Math Anal Appl 2008], [Sci China Ser A 2009], Liu[Rocky Mountain J Math 2011], Cui-Yang[Acta Math Sci Ser B 2013], Chen[Complex Var Elliptic Equ 2013], Wang-Liu-Fang[Acta Math. Sinica (Chinese Ser) 2016].</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645730","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
Integrable geodesic flow in 3D and webs of maximal rank 三维可积分大地流和最大秩网
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-11 DOI: 10.1007/s13324-024-00987-y
Sergey I. Agafonov
{"title":"Integrable geodesic flow in 3D and webs of maximal rank","authors":"Sergey I. Agafonov","doi":"10.1007/s13324-024-00987-y","DOIUrl":"10.1007/s13324-024-00987-y","url":null,"abstract":"<div><p>We characterize geodesic flows, admitting two commuting quadratic integrals with common principal directions, in terms of the geodesic 4-webs such that the tangents to the web leaves are common zero directions of the integrals. We prove that, under some natural geometric hypothesis, the metric is of Stäckel type.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142600559","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 entire solutions of certain partial differential equations 论某些偏微分方程的全解
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-09 DOI: 10.1007/s13324-024-00988-x
Feng Lü, Wenqi Bi
{"title":"On entire solutions of certain partial differential equations","authors":"Feng Lü,&nbsp;Wenqi Bi","doi":"10.1007/s13324-024-00988-x","DOIUrl":"10.1007/s13324-024-00988-x","url":null,"abstract":"<div><p>We firstly describe entire solutions of variation of the well-known PDE of tubular surfaces. In addition, we consider entire solutions of certain partial differential equations, which are related with the Picard’s little theorem. Moreover, we obtain a Tumura-Clunie type theorem in <span>({mathbb {C}}^{m})</span>, which is an improvement of a result given by Hu-Yang (Bull Aust Math Soc 90: 444-456, 2014).</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142598863","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
Multiple nontrivial solutions for a double phase system with concave-convex nonlinearities in subcritical and critical cases 具有凹凸非线性的双相系统在次临界和临界情况下的多个非微妙解
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-06 DOI: 10.1007/s13324-024-00985-0
Yizhe Feng, Zhanbing Bai
{"title":"Multiple nontrivial solutions for a double phase system with concave-convex nonlinearities in subcritical and critical cases","authors":"Yizhe Feng,&nbsp;Zhanbing Bai","doi":"10.1007/s13324-024-00985-0","DOIUrl":"10.1007/s13324-024-00985-0","url":null,"abstract":"<div><p>In this article, we study the double phase elliptic system which contain with the parametric concave-convex nonlinearities and critical growth. The introduction of mixed critical terms brings some difficulties to the problem. For example, in proving that the solution is nontrivial, we need to do an additional series of studies on scalar equation. By introducing a new optimal constant <span>(S_{alpha ,beta })</span> in the double phase system, considering the different magnitude relationships of the exponential terms, and using the fibering method in form of the Nehari manifold and the Brezis-Lieb Lemma, the existence and multiplicity of solutions in subcritical and critical cases are obtained separately.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587791","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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