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Outgoing monotone geodesics of standard subspaces 标准子空间的出线单调测地线
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-03-30 DOI: 10.1007/s13324-026-01187-6
Jonas Schober
{"title":"Outgoing monotone geodesics of standard subspaces","authors":"Jonas Schober","doi":"10.1007/s13324-026-01187-6","DOIUrl":"10.1007/s13324-026-01187-6","url":null,"abstract":"<div><p>We prove a real version of the Lax–Phillips Theorem and classify outgoing reflection positive orthogonal one-parameter groups. Using these results, we provide a normal form for outgoing monotone geodesics in the set <span>(textrm{Stand}(mathcal {H}))</span> of standard subspaces on some complex Hilbert space <span>(mathcal {H})</span>. As the modular operators of a standard subspace are closely related to positive Hankel operators, our results are obtained by constructing some explicit symbols for positive Hankel operators. We also describe which of the monotone geodesics in <span>(textrm{Stand}(mathcal {H}))</span> arise from the unitary one-parameter groups described in Borchers’ Theorem and provide explicit examples of monotone geodesics that are not of this type.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147607405","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
Second Hankel determinant and coefficient problems in a set of analytic functions 第二，分析函数集中的汉克尔行列式和系数问题
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1007/s13324-026-01192-9
Edyta Trybucka
{"title":"Second Hankel determinant and coefficient problems in a set of analytic functions","authors":"Edyta Trybucka","doi":"10.1007/s13324-026-01192-9","DOIUrl":"10.1007/s13324-026-01192-9","url":null,"abstract":"<div><p>In this paper we consider the class of functions <i>f</i> analytic in the open unit disc <span>(|z|&lt;1)</span> with the normalization <span>(f(0)=f'(0)-1=0)</span> that satisfy the condition <span>( zf'(z)=G(z)P(z))</span> for some odd function <i>G</i> and some function <i>P</i> with positive real part and with certain restrictions on they Taylor’s coefficients. For this class we establish the bounds for the coefficients and for the Fekete-Szegö functional. Moreover, the sharp bound of the second Hankel determinant is found.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561587","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 to: Fourier method for the Neumann problem on a torus 修正：环面上诺伊曼问题的傅立叶方法
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1007/s13324-026-01167-w
Z. Ashtab, J. Morais, R. Michael Porter
{"title":"Correction to: Fourier method for the Neumann problem on a torus","authors":"Z. Ashtab,&nbsp;J. Morais,&nbsp;R. Michael Porter","doi":"10.1007/s13324-026-01167-w","DOIUrl":"10.1007/s13324-026-01167-w","url":null,"abstract":"","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01167-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561586","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
Geometric scattering for nonlinear wave equations on the Schwarzschild metric 史瓦西度规上非线性波动方程的几何散射
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-03-23 DOI: 10.1007/s13324-026-01181-y
Pham Truong Xuan
{"title":"Geometric scattering for nonlinear wave equations on the Schwarzschild metric","authors":"Pham Truong Xuan","doi":"10.1007/s13324-026-01181-y","DOIUrl":"10.1007/s13324-026-01181-y","url":null,"abstract":"<div><p>In this paper, we establish a conformal scattering theory for defocusing semilinear wave equations on Schwarzschild spacetime. We combine the energy and pointwise decay results for solutions obtained in [19] with a Sobolev embedding on spacelike hypersurfaces to derive two-sided energy estimates between the energy flux of solutions through the Cauchy initial hypersurface <span>(Sigma _0 = { t = 0 })</span> and that through the null conformal boundaries <span>(mathfrak {H}^+ cup {mathscr {I}}^+)</span> (respectively, <span>(mathfrak {H}^- cup {mathscr {I}}^-)</span>). By combining these estimates with the well-posedness of the Cauchy and Goursat problems for nonlinear wave equations, we construct a bounded linear and locally Lipschitz scattering operator that maps past scattering data to future scattering data.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561138","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 weighted spectral quantum fidelity 加权谱量子保真度
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-03-23 DOI: 10.1007/s13324-026-01180-z
Cong Trinh Le, The Khoi Vu, Minh Toan Ho, Trung Hoa Dinh
{"title":"A weighted spectral quantum fidelity","authors":"Cong Trinh Le,&nbsp;The Khoi Vu,&nbsp;Minh Toan Ho,&nbsp;Trung Hoa Dinh","doi":"10.1007/s13324-026-01180-z","DOIUrl":"10.1007/s13324-026-01180-z","url":null,"abstract":"<div><p>We introduce and study a one-parameter family of fidelity-type quantities based on the weighted spectral geometric mean, which we call the <i>weighted spectral fidelity</i> <span>( textsf{F}_t^{text {spec}}(rho ,sigma ):=operatorname {Tr}!big [rho (rho ^{-1}sharp sigma )^{2t}big ], tin [0,1]. )</span> This family interpolates smoothly between the trivial overlap (<span>(t=0,1)</span>) and the Uhlmann (root) fidelity at <span>(t=tfrac{1}{2})</span>, and it is distinct from the sandwiched Rényi family except at this midpoint. We establish core structural features-unitary invariance, tensor stabilization and multiplicativity, flip symmetry, endpoint behavior, and a orthogonality criterion. We further show explicit <i>violations of DPI</i> for generic <span>(tne tfrac{1}{2})</span>. For concavity in the state variables we obtain concavity in each variable separately. Closed forms are obtained for pure states and for qubits in Bloch coordinates. We also extend the first Fuchs–van de Graaf inequality to <span>(textsf{F}_t^{text {spec}})</span> for all <span>(tin [0,1])</span>, while the second inequality fails away from the midpoint.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561136","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
Gradient Hölder regularity for weak solutions of nonlinear sub-elliptic systems with drift terms in the Heisenberg group Heisenberg群中具有漂移项的非线性亚椭圆系统弱解的梯度Hölder正则性
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-03-23 DOI: 10.1007/s13324-026-01184-9
Jialin Wang, Guoqiang Duan, Dongni Liao
{"title":"Gradient Hölder regularity for weak solutions of nonlinear sub-elliptic systems with drift terms in the Heisenberg group","authors":"Jialin Wang,&nbsp;Guoqiang Duan,&nbsp;Dongni Liao","doi":"10.1007/s13324-026-01184-9","DOIUrl":"10.1007/s13324-026-01184-9","url":null,"abstract":"<div><p>This paper is devoted to establishing the optimal gradient Hölder regularity for weak solutions to nonlinear sub-elliptic systems with drift terms for the super-quadratic growth, under controllable structure conditions and natural structure conditions in the Heisenberg group, respectively. The technique of <span>(mathcal {A})</span>-harmonic approximation introduced by Simon and developed by Duzaar and Grotowski is adapted to our context, and then several <span>(Gamma ^{1,gamma } (0&lt;gamma &lt;1))</span> regularity results are obtained in the sense of the Folland-Stein space. In particular, we establish the optimal Hölder exponent for horizontal gradients of vector-valued weak solutions on its regular set directly. The primary model covered by our analysis is the non-degenerate sub-elliptic <i>p</i>-Laplacian system with the drift term.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561137","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
Normalized ground states for the inhomogeneous Schrödinger equation with mixed fractional Laplacians 混合分数阶拉普拉斯不等式Schrödinger方程的归一化基态
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-03-21 DOI: 10.1007/s13324-026-01185-8
Jie Yang, Haibo Chen
{"title":"Normalized ground states for the inhomogeneous Schrödinger equation with mixed fractional Laplacians","authors":"Jie Yang,&nbsp;Haibo Chen","doi":"10.1007/s13324-026-01185-8","DOIUrl":"10.1007/s13324-026-01185-8","url":null,"abstract":"<div><p>In this paper, we study the inhomogeneous Schrödinger equation with mixed fractional Laplacians and critical exponent, which arises in the population dynamics model with nonlocal diffusion. We prove the existence of normalized solutions via a generalized version of Lieb’s translation theorem and local minimizing method.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561254","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 a certain subclass of strongly starlike functions 强星形函数的一个子类
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-03-19 DOI: 10.1007/s13324-026-01188-5
Rahim Kargar, Janusz Sokół, Hesam Mahzoon
{"title":"On a certain subclass of strongly starlike functions","authors":"Rahim Kargar,&nbsp;Janusz Sokół,&nbsp;Hesam Mahzoon","doi":"10.1007/s13324-026-01188-5","DOIUrl":"10.1007/s13324-026-01188-5","url":null,"abstract":"<div><p>Let <span>(mathcal {S}^*(alpha _1,alpha _2))</span>, where <span>( alpha _1, alpha _2 in (0,1])</span>, represent the class of functions <i>f</i> that are analytic in the open unit disk <span>(mathbb {D})</span>, normalized by <span>(f(0) = f'(0) - 1=0)</span>, and satisfying the following double-sided inequality: </p><div><div><span>$$begin{aligned} -frac{pi alpha _1}{2}&lt; arg left{ frac{zf'(z)}{f(z)}right} &lt;frac{pi alpha _2}{2}, quad (zin mathbb {D}). end{aligned}$$</span></div></div><p>In this manuscript, we estimate the coefficients and logarithmic coefficients associated with functions that belong to the class <span>(mathcal {S}^*(alpha _1,alpha _2))</span>. As a result, we provide a general bound for the coefficients of a strongly starlike function, which has been an open question until now. Finally, we derive upper and lower bounds for the expression <span>(textrm{Re}{zf'(z)/f(z)})</span>, where <span>(fin mathcal {S}^*(alpha _1,alpha _2))</span>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01188-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560242","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
On the generalised attenuated X-ray transform of planar tensor fields 平面张量场的广义衰减x射线变换
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-03-19 DOI: 10.1007/s13324-026-01164-z
David Omogbhe
{"title":"On the generalised attenuated X-ray transform of planar tensor fields","authors":"David Omogbhe","doi":"10.1007/s13324-026-01164-z","DOIUrl":"10.1007/s13324-026-01164-z","url":null,"abstract":"<div><p>We present an explicit inversion method that stably reconstructs smooth, real-valued, symmetric tensor fields compactly supported in the plane from knowledge of their generalised attenuated X-ray transform.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560416","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
Localized concentration of semiclassical solutions for double phase problems with nonlocal reaction 非局域反应双相问题半经典解的局域浓度
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-03-18 DOI: 10.1007/s13324-026-01182-x
Jian Zhang, Wen Zhang, Vicenţiu D Rădulescu
{"title":"Localized concentration of semiclassical solutions for double phase problems with nonlocal reaction","authors":"Jian Zhang,&nbsp;Wen Zhang,&nbsp;Vicenţiu D Rădulescu","doi":"10.1007/s13324-026-01182-x","DOIUrl":"10.1007/s13324-026-01182-x","url":null,"abstract":"<div><p>This paper focuses on the study of multiplicity and localized concentration properties of positive solutions for the following singularly perturbed double phase problem with nonlocal Choquard reaction </p><div><div><span>$$begin{aligned} left{ begin{array}{ll} -epsilon ^{p}Delta _{p} u-epsilon ^{q}Delta _{q} u +V(x)(|u|^{p-2}u+|u|^{q-2}u) quad =epsilon ^{mu -N}left( frac{1}{|x|^{mu }}*G(u)right) g(u),&amp; hbox {in}~mathbb {R}^{N}, uin W^{1,p}(mathbb {R}^{N})cap W^{1,q}(mathbb {R}^{N}),u&gt;0, &amp; hbox {in}~mathbb {R}^{N}, end{array} right. end{aligned}$$</span></div></div><p>where <span>(1&lt; p&lt;q&lt;N)</span>, <span>(0&lt;mu &lt;p)</span>, <span>(epsilon )</span> is a small positive parameter and <i>V</i> is the absorption potential. We assume that the potential <i>V</i> satisfies only a local condition introduced by del Pino and Felmer. Applying suitable variational and topological methods combined with penalization technique, we obtain multiple semiclassical positive solutions for <span>(epsilon &gt;0)</span> sufficiently small as well as related concentration properties, in relationship with the set where the potential <i>V</i> attains its minimum. Moreover, we also investigate the decay property of semiclassical positive solutions. The main results included in this paper complement several recent contributions to the study of concentration phenomena.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01182-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559876","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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