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Spectral properties of the gradient operator with nonconstant coefficients 具有非恒定系数的梯度算子的谱特性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-09-18 DOI: 10.1007/s13324-024-00966-3
F. Colombo, F. Mantovani, P. Schlosser
{"title":"Spectral properties of the gradient operator with nonconstant coefficients","authors":"F. Colombo,&nbsp;F. Mantovani,&nbsp;P. Schlosser","doi":"10.1007/s13324-024-00966-3","DOIUrl":"10.1007/s13324-024-00966-3","url":null,"abstract":"<div><p>In mathematical physics, the gradient operator with nonconstant coefficients encompasses various models, including Fourier’s law for heat propagation and Fick’s first law, that relates the diffusive flux to the gradient of the concentration. Specifically, consider <span>(nge 3)</span> orthogonal unit vectors <span>(e_1,ldots ,e_nin {mathbb {R}}^n)</span>, and let <span>(Omega subseteq {mathbb {R}}^n)</span> be some (in general unbounded) Lipschitz domain. This paper investigates the spectral properties of the gradient operator <span>(T=sum _{i=1}^ne_ia_i(x)frac{partial }{partial x_i})</span> with nonconstant positive coefficients <span>(a_i:{overline{Omega }}rightarrow (0,infty ))</span>. Under certain regularity and growth conditions on the <span>(a_i)</span>, we identify bisectorial or strip-type regions that belong to the <i>S</i>-resolvent set of <i>T</i>. Moreover, we obtain suitable estimates of the associated resolvent operator. Our focus lies in the spectral theory on the <i>S</i>-spectrum, designed to study the operators acting in Clifford modules <i>V</i> over the Clifford algebra <span>({mathbb {R}}_n)</span>, with vector operators being a specific crucial subclass. The spectral properties related to the <i>S</i>-spectrum of <i>T</i> are linked to the inversion of the operator <span>(Q_s(T):=T^2-2s_0T+|s|^2)</span>, where <span>(sin {mathbb {R}}^{n+1})</span> is a paravector, i.e., it is of the form <span>(s=s_0+s_1e_1+cdots +s_ne_n)</span>. This spectral problem is substantially different from the complex one, since it allows to associate general boundary conditions to <span>(Q_s(T))</span>, i.e., to the squared operator <span>(T^2)</span>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00966-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142263837","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 note on closed quasi-Einstein manifolds 关于封闭的准爱因斯坦流形的说明
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-09-17 DOI: 10.1007/s13324-024-00967-2
Wagner Oliveira Costa-Filho
{"title":"A note on closed quasi-Einstein manifolds","authors":"Wagner Oliveira Costa-Filho","doi":"10.1007/s13324-024-00967-2","DOIUrl":"10.1007/s13324-024-00967-2","url":null,"abstract":"<div><p>The notion of <i>m</i>-quasi-Einstein manifolds originates from the study of Einstein warped product metrics and they are influential in constructing for many physical models. For example, these manifolds arises for extremal isolated horizons in the theory of black holes. In a recent work by Cochran (arXiv:2404.17090v1, 2024), the author studied Killing vector fields on closed <i>m</i>-quasi-Einstein manifolds. In this short paper, we will give another proof of his main result involving the scalar curvature, which holds for all values of <i>m</i> and is based on the use of known formulae related to quasi-Einstein metrics.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142263845","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 odd univalent harmonic mappings 关于奇数单值谐波映射
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-09-04 DOI: 10.1007/s13324-024-00964-5
Kapil Jaglan, Anbareeswaran Sairam Kaliraj
{"title":"On odd univalent harmonic mappings","authors":"Kapil Jaglan,&nbsp;Anbareeswaran Sairam Kaliraj","doi":"10.1007/s13324-024-00964-5","DOIUrl":"10.1007/s13324-024-00964-5","url":null,"abstract":"<div><p>Odd univalent analytic functions played an instrumental role in the proof of the celebrated Bieberbach conjecture. In this article, we explore odd univalent harmonic mappings, focusing on coefficient estimates, growth and distortion theorems. Motivated by the unresolved harmonic analogue of the Bieberbach conjecture, we investigate specific subclasses of <span>({mathcal {S}}^0_H)</span>, the class of sense-preserving univalent harmonic functions. We provide sharp coefficient bounds for functions exhibiting convexity in one direction and extend our findings to a more generalized class including the major geometric subclasses of <span>({mathcal {S}}^0_H)</span>. Additionally, we analyze the inclusion of these functions in Hardy spaces and broaden the range of <i>p</i> for which they belong. In particular, the results of this article enhance understanding and highlight analogous growth patterns between odd univalent harmonic functions and the harmonic Bieberbach conjecture. We conclude the article with 2 conjectures and possible scope for further study as well.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222483","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
Feynman formulas for qp- and pq-quantization of some Vladimirov type time-dependent Hamiltonians on finite adeles 有限阿德尔上某些弗拉基米洛夫型时变哈密顿的 qp 和 pq 量化的费曼公式
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-08-27 DOI: 10.1007/s13324-024-00965-4
Roman Urban
{"title":"Feynman formulas for qp- and pq-quantization of some Vladimirov type time-dependent Hamiltonians on finite adeles","authors":"Roman Urban","doi":"10.1007/s13324-024-00965-4","DOIUrl":"10.1007/s13324-024-00965-4","url":null,"abstract":"<div><p>Let <i>Q</i> be the <i>d</i>-dimensional space of finite adeles over the algebraic number field <i>K</i> and let <span>(P=Q^*)</span> be its dual space. For a certain type of Vladimirov type time-dependent Hamiltonian <span>(H_V(t):Qtimes Prightarrow {mathbb {C}})</span> we construct the Feynman formulas for the solution of the Cauchy problem with the Schrödinger operator <img> where the caret operator stands for the <i>qp</i>- or <i>pq</i>-quantization.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00965-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222499","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
Two-component integrable extension of general heavenly equation 一般天体方程的两分量可积分扩展
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-08-20 DOI: 10.1007/s13324-024-00961-8
Wojciech Kryński, Artur Sergyeyev
{"title":"Two-component integrable extension of general heavenly equation","authors":"Wojciech Kryński,&nbsp;Artur Sergyeyev","doi":"10.1007/s13324-024-00961-8","DOIUrl":"10.1007/s13324-024-00961-8","url":null,"abstract":"<div><p>We introduce an integrable two-component extension of the general heavenly equation and prove that the solutions of this extension are in one-to-one correspondence with 4-dimensional hyper-para-Hermitian metrics. Furthermore, we demonstrate that if the metrics in question are hyper-para-Kähler, then our system reduces to the general heavenly equation. We also present an infinite hierarchy of nonlocal symmetries, as well as a recursion operator, for the system under study.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00961-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222562","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
Monotonicity patterns and functional inequalities for modified Lommel functions of the first kind 修正的第一类洛梅尔函数的单调性模式和函数不等式
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-08-17 DOI: 10.1007/s13324-024-00962-7
H. M. Zayed, K. Mehrez, J. Morais
{"title":"Monotonicity patterns and functional inequalities for modified Lommel functions of the first kind","authors":"H. M. Zayed,&nbsp;K. Mehrez,&nbsp;J. Morais","doi":"10.1007/s13324-024-00962-7","DOIUrl":"10.1007/s13324-024-00962-7","url":null,"abstract":"<div><p>We present new functional inequalities and monotonicity results for the modified Lommel functions of the first kind, such as absolute monotonicity, complete monotonicity, monotonicity, log-convexity, and strong convexity. Various inequalities involving reverse Turán-type inequalities are proven to illustrate the results of this paper.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222485","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
Existence and multiplicity of solutions for the Schrödinger–Poisson equation with prescribed mass 具有规定质量的薛定谔-泊松方程的解的存在性和多重性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-08-16 DOI: 10.1007/s13324-024-00963-6
Xueqin Peng
{"title":"Existence and multiplicity of solutions for the Schrödinger–Poisson equation with prescribed mass","authors":"Xueqin Peng","doi":"10.1007/s13324-024-00963-6","DOIUrl":"10.1007/s13324-024-00963-6","url":null,"abstract":"<div><p>In this paper, we study the existence and multiplicity for the following Schrödinger–Poisson equation </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} -Delta u+lambda u-kappa (|x|^{-1}*|u|^2)u=f(u),&amp;{}text {in}~~{mathbb {R}}^{3}, u&gt;0,~displaystyle int _{{mathbb {R}}^{3}}u^2dx=a^2, end{array}right. } end{aligned}$$</span></div></div><p>where <span>(a&gt;0)</span> is a prescribed mass, <span>(kappa in {mathbb {R}}setminus {0})</span> and <span>(lambda in {mathbb {R}})</span> is an undetermined parameter which appears as a Lagrange multiplier. Our results are threefold: (i) for the case <span>(kappa &lt;0)</span>, we obtain the normalized ground state solution for <span>(a&gt;0)</span> small by working on the Pohozaev manifold, where <i>f</i> satisfies the <span>(L^2)</span>-supercritical and Sobolev subcritical conditions, and the behavior of the normalized ground state energy <span>(c_a)</span> is also obtained; (ii) we prove that the above equation possesses infinitely many radial solutions whose energy converges to infinity; (iii) for <span>(kappa &gt;0)</span> and <span>(f(u)=|u|^{4}u)</span>, we revisit the Brézis–Nirenberg problem with a nonlocal perturbation and obtain infinitely many radial solutions with negative energy. Our results implement some existing results about the Schrödinger–Poisson equation in the <span>(L^2)</span>-constraint setting.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222487","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
Analysing Milne-type inequalities by using tempered fractional integrals 利用回火分式积分分析米尔恩型不等式
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-08-14 DOI: 10.1007/s13324-024-00958-3
Wali Haider, Hüseyin Budak, Asia Shehzadi, Fatih Hezenci, Haibo Chen
{"title":"Analysing Milne-type inequalities by using tempered fractional integrals","authors":"Wali Haider,&nbsp;Hüseyin Budak,&nbsp;Asia Shehzadi,&nbsp;Fatih Hezenci,&nbsp;Haibo Chen","doi":"10.1007/s13324-024-00958-3","DOIUrl":"10.1007/s13324-024-00958-3","url":null,"abstract":"<div><p>In this research, we define an essential identity for differentiable functions in the framework of tempered fractional integral. By utilizing this identity, we deduce several modifications of fractional Milne-type inequalities. We provide novel expansions of Milne-type inequalities in the domain of tempered fractional integrals. The investigation emphasises important functional categories, including convex functions, bounded functions, Lipschitzian functions, and functions with bounded variation.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222486","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
Groundstates of a magnetic critical Choquard Poisson system with multiple potentials 具有多电势的磁临界乔夸德泊松系的基态
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-08-07 DOI: 10.1007/s13324-024-00959-2
Wenjing Chen, Zexi Wang
{"title":"Groundstates of a magnetic critical Choquard Poisson system with multiple potentials","authors":"Wenjing Chen,&nbsp;Zexi Wang","doi":"10.1007/s13324-024-00959-2","DOIUrl":"10.1007/s13324-024-00959-2","url":null,"abstract":"<div><p>In this article, we establish the existence of ground state solutions for a magnetic critical Choquard Poisson system with multiple potentials by variational methods.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929797","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
Generalization of quantum calculus and corresponding Hermite–Hadamard inequalities 量子微积分的广义化和相应的赫米特-哈达马德不等式
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-08-06 DOI: 10.1007/s13324-024-00960-9
Saira Bano Akbar, Mujahid Abbas, Hüseyin Budak
{"title":"Generalization of quantum calculus and corresponding Hermite–Hadamard inequalities","authors":"Saira Bano Akbar,&nbsp;Mujahid Abbas,&nbsp;Hüseyin Budak","doi":"10.1007/s13324-024-00960-9","DOIUrl":"10.1007/s13324-024-00960-9","url":null,"abstract":"<div><p>The aim of this paper is first to introduce generalizations of quantum integrals and derivatives which are called <span>((phi ,-,h))</span> integrals and <span>((phi ,-,h))</span> derivatives, respectively. Then we investigate some implicit integral inequalities for <span>((phi ,-,h))</span> integrals. Different classes of convex functions are used to prove these inequalities for symmetric functions. Under certain assumptions, Hermite–Hadamard-type inequalities for <i>q</i>-integrals are deduced. The results presented herein are applicable to convex, <i>m</i>-convex, and <span>(hbar )</span>-convex functions defined on the non-negative part of the real line.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00960-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929812","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
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