Analysis and Mathematical Physics最新文献_第4页

Some remarks on Shanks-type conjectures 关于香克斯类猜想的一些评论

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2024-08-05 DOI: 10.1007/s13324-024-00951-w

Christopher Felder

引用次数: 0

Schrödinger equation with finitely many (delta )-interactions: closed form, integral and series representations for solutions 具有有限多个 $$delta $$ 相互作用的薛定谔方程：解的闭合形式、积分和序列表示法

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2024-08-03 DOI: 10.1007/s13324-024-00957-4

Vladislav V. Kravchenko, Víctor A. Vicente-Benítez

{"title":"Schrödinger equation with finitely many (delta )-interactions: closed form, integral and series representations for solutions","authors":"Vladislav V. Kravchenko, Víctor A. Vicente-Benítez","doi":"10.1007/s13324-024-00957-4","DOIUrl":"10.1007/s13324-024-00957-4","url":null,"abstract":"<div>A closed form solution for the one-dimensional Schrödinger equation with a finite number of (delta )-interactions <div><div>$$begin{aligned} {textbf{L}}_{q,{mathfrak {I}}_{N}}y:=-y^{prime prime }+left( q(x)+sum _{k=1}^{N}alpha _{k}delta (x-x_{k})right) y=lambda y,quad 0<x<b,;lambda in {mathbb {C}} end{aligned}$$</div></div>is presented in terms of the solution of the unperturbed equation <div><div>$$begin{aligned} {textbf{L}}_{q}y:=-y^{prime prime }+q(x)y=lambda y,quad 0<x<b,;lambda in {mathbb {C}} end{aligned}$$</div></div>and a corresponding transmutation (transformation) operator ({textbf{T}}_{{mathfrak {I}}_{N}}^{f}) is obtained in the form of a Volterra integral operator. With the aid of the spectral parameter power series method, a practical construction of the image of the transmutation operator on a dense set is presented, and it is proved that the operator ({textbf{T}}_{{mathfrak {I}}_{N}}^{f}) transmutes the second derivative into the Schrödinger operator ({textbf{L}}_{q,{mathfrak {I}}_{N}}) on a Sobolev space (H^{2}). A Fourier-Legendre series representation for the integral transmutation kernel is developed, from which a new representation for the solutions and their derivatives, in the form of a Neumann series of Bessel functions, is derived.</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929811","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 existence of radially symmetric solutions to p-k-Hessian equations and systems 论 p-k-Hessian 方程和系统的径向对称解的存在性

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2024-08-02 DOI: 10.1007/s13324-024-00953-8

Ling Mi, YangYang Ji

引用次数: 0

Ill-posedness for the Camassa–Holm equation in (B_{p,1}^{1}cap C^{0,1}) $$B_{p,1}^{1}cap C^{0,1}$$ 中的卡马萨-霍尔姆方程的失摆问题

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2024-08-02 DOI: 10.1007/s13324-024-00956-5

Jinlu Li, Yanghai Yu, Yingying Guo, Weipeng Zhu

引用次数: 0

Fractional maximal operators on weighted variable Lebesgue spaces over the spaces of homogeneous type 同质类型空间上加权可变勒贝格空间的分数最大算子

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1007/s13324-024-00955-6

Xi Cen

引用次数: 0

Normalized solution to p-Kirchhoff-type equation in (mathbb {R}^{N}) p-Kirchhoff 型方程在 $$mathbb {R}^{N}$$ 中的归一化解

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2024-07-31 DOI: 10.1007/s13324-024-00954-7

ZhiMin Ren, YongYi Lan

引用次数: 0

Regularity and continuity of higher order maximal commutators 高阶最大换元器的正则性和连续性

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2024-07-31 DOI: 10.1007/s13324-024-00952-9

Feng Liu, Yuan Ma

{"title":"Regularity and continuity of higher order maximal commutators","authors":"Feng Liu, Yuan Ma","doi":"10.1007/s13324-024-00952-9","DOIUrl":"10.1007/s13324-024-00952-9","url":null,"abstract":"<div>Let (kge 1), (0le alpha <d) and (mathfrak {M}_{b,alpha }^k) be the k-th order fractional maximal commutator. When (alpha =0), we denote (mathfrak {M}_{b,alpha }^k=mathfrak {M}_{b}^k). We show that (mathfrak {M}_{b,alpha }^k) is bounded from the first order Sobolev space (W^{1,p_1}(mathbb {R}^d)) to (W^{1,p}(mathbb {R}^d)) where (1<p_1,p_2,p<infty ), (1/p=1/p_1+k/p_2-alpha /d). We also prove that if (0<s<1), (1<p_1,p_2,p,q<infty ) and (1/p=1/p_1+k/p_2), then (mathfrak {M}_b^k) is bounded and continuous from the fractional Sobolev space (W^{s,p_1}(mathbb {R}^d)) to ({W^{s,p}(mathbb {R}^d)}) if (bin W^{s,p_2}(mathbb {R}^d)), from the inhomogeneous Triebel–Lizorkin space (F_s^{p_1,q}(mathbb {R}^d)) to (F_s^{p,q}(mathbb {R}^d)) if (bin F_s^{p_2,q} (mathbb {R}^d)) and from the inhomogeneous Besov space (B_s^{p_1,q}(mathbb {R}^d)) to (B_s^{p,q}(mathbb {R}^d)) if (bin B_s^{p_2,q}(mathbb {R}^d)). It should be pointed out that the main ingredients of proving the above results are some refined and complex difference estimates of higher order maximal commutators as well as some characterizations of the Sobolev spaces, Triebel–Lizorkin spaces and Besov spaces.</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141865186","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

Exponential polynomials as solutions of certain type binomial differential equations 指数多项式作为某类二项式微分方程的解

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2024-07-21 DOI: 10.1007/s13324-024-00949-4

Linkui Gao, Changjiang Song

引用次数: 0

Inverse parameter and shape problem for an isotropic scatterer with two conductivity coefficients 具有两个传导系数的各向同性散射体的反参数和形状问题

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2024-07-19 DOI: 10.1007/s13324-024-00950-x

Rafael Ceja Ayala, Isaac Harris, Andreas Kleefeld

引用次数: 0

Sobolev orthogonal polynomials, Gauss–Borel factorization and perturbations 索波列正交多项式、高斯-伯尔因式分解和扰动