Analysis and Mathematical Physics最新文献_第2页

A refined upper bound for the third Hankel determinant of univalent functions 一元函数的第三汉克尔行列式的改进上界

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1007/s13324-026-01274-8

Boban Karapetrović

引用次数: 0

Exact spectral solutions of Pöschl–Teller potentials via trigonometric and hyperbolic Dunkl operators 通过三角和双曲邓克尔算子的Pöschl-Teller势的精确谱解

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-09-21 DOI: 10.1007/s13324-026-01271-x

Nalan Kandirmaz

{"title":"Exact spectral solutions of Pöschl–Teller potentials via trigonometric and hyperbolic Dunkl operators","authors":"Nalan Kandirmaz","doi":"10.1007/s13324-026-01271-x","DOIUrl":"10.1007/s13324-026-01271-x","url":null,"abstract":"<div>Exact analytical solutions of the Schrödinger equation were derived for the symmetric trigonometric and hyperbolic Pöschl–Teller (PT) potentials using geometry-compatible trigonometric and hyperbolic Dunkl operators. In rational Dunkl operator formulations, inverse-square singularities arise from the geometric mismatch between the deformation kernel and the potential structure, destroying exact solvability and forcing Pekeris-type approximation schemes. By employing geometry-compatible operators, these singularities were eliminated at the operator level and exact solvability was restored without any approximation. The trigonometric and hyperbolic Dunkl operators, although rigorously defined in the mathematical literature, have not been systematically applied to quantum mechanical potential problems; the present work addressed this gap and identified operator–geometry compatibility as a key condition for exact solvability in Dunkl-deformed systems. Within the supersymmetric quantum mechanics framework, closed-form parity-resolved energy spectra and eigenfunctions were obtained in terms of Jacobi polynomials, and shape invariance was established to be preserved exactly under the deformation. The geometry-compatible Hilbert space weights (|sin (alpha x)|^{2mu }) and (|sinh (alpha x)|^{2mu }) were derived, replacing the rational Dunkl weight (|x|^{2mu }). The corrected SUSY hierarchy exhibits alternating parity at successive steps, and the Jacobi-polynomial eigenfunctions depend explicitly on (mu ). The exact Robertson uncertainty lower bound is eigenstate-dependent; its simple near-origin form is only an approximation.</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149034721","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

Exact spectral solutions of Pöschl–Teller potentials via trigonometric and hyperbolic Dunkl operators 通过三角和双曲邓克尔算子的Pöschl-Teller势的精确谱解

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-09-21 DOI: 10.1007/s13324-026-01271-x

Nalan Kandirmaz

{"title":"Exact spectral solutions of Pöschl–Teller potentials via trigonometric and hyperbolic Dunkl operators","authors":"Nalan Kandirmaz","doi":"10.1007/s13324-026-01271-x","DOIUrl":"10.1007/s13324-026-01271-x","url":null,"abstract":"<div>Exact analytical solutions of the Schrödinger equation were derived for the symmetric trigonometric and hyperbolic Pöschl–Teller (PT) potentials using geometry-compatible trigonometric and hyperbolic Dunkl operators. In rational Dunkl operator formulations, inverse-square singularities arise from the geometric mismatch between the deformation kernel and the potential structure, destroying exact solvability and forcing Pekeris-type approximation schemes. By employing geometry-compatible operators, these singularities were eliminated at the operator level and exact solvability was restored without any approximation. The trigonometric and hyperbolic Dunkl operators, although rigorously defined in the mathematical literature, have not been systematically applied to quantum mechanical potential problems; the present work addressed this gap and identified operator–geometry compatibility as a key condition for exact solvability in Dunkl-deformed systems. Within the supersymmetric quantum mechanics framework, closed-form parity-resolved energy spectra and eigenfunctions were obtained in terms of Jacobi polynomials, and shape invariance was established to be preserved exactly under the deformation. The geometry-compatible Hilbert space weights (|sin (alpha x)|^{2mu }) and (|sinh (alpha x)|^{2mu }) were derived, replacing the rational Dunkl weight (|x|^{2mu }). The corrected SUSY hierarchy exhibits alternating parity at successive steps, and the Jacobi-polynomial eigenfunctions depend explicitly on (mu ). The exact Robertson uncertainty lower bound is eigenstate-dependent; its simple near-origin form is only an approximation.</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149034722","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

Biquaternion offset linear canonical Stockwell transform and associated uncertainty principles with application of signal recovery 双四元数偏移线性正则斯托克韦尔变换及其不确定性原理与信号恢复的应用

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-09-17 DOI: 10.1007/s13324-026-01272-w

Akhilesh Prasad, Pratiksha Moond, Manab Kundu

{"title":"Biquaternion offset linear canonical Stockwell transform and associated uncertainty principles with application of signal recovery","authors":"Akhilesh Prasad, Pratiksha Moond, Manab Kundu","doi":"10.1007/s13324-026-01272-w","DOIUrl":"10.1007/s13324-026-01272-w","url":null,"abstract":"<div>Motivated by the rapid growth of modern signal processing applications and efficient mathematical tools that can handle multidimensional, nonstationary and shifted signals in a unified manner, this paper introduces a new transform, called the biquaternion offset linear canonical Stockwell transform (BiQOLCST). The proposed framework extends existing transform techniques and provides a flexible approach for analyzing complex signal structures. Several important properties of the transform are established, including linearity, anti-linearity, boundedness, shift and modulation properties, orthogonality relations and the reconstruction formula. In addition, Heisenberg, logarithmic and Donoho-Stark uncertainty principles are derived for the proposed transform, highlighting its inherent limits of simultaneous localization in different domains. These results also demonstrate the usefulness of the BiQOLCST in signal representation, analysis and recovery. Furthermore, signal reconstruction is investigated using the Donoho-Stark uncertainty principle, which provides theoretical conditions for the reliable recovery of signals from incomplete information. The potential applications in color image processing and in the analysis of non-stationary signals are explored.\u0000</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986668","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

Biquaternion offset linear canonical Stockwell transform and associated uncertainty principles with application of signal recovery 双四元数偏移线性正则斯托克韦尔变换及其不确定性原理与信号恢复的应用

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-09-17 DOI: 10.1007/s13324-026-01272-w

Akhilesh Prasad, Pratiksha Moond, Manab Kundu

{"title":"Biquaternion offset linear canonical Stockwell transform and associated uncertainty principles with application of signal recovery","authors":"Akhilesh Prasad, Pratiksha Moond, Manab Kundu","doi":"10.1007/s13324-026-01272-w","DOIUrl":"10.1007/s13324-026-01272-w","url":null,"abstract":"<div>Motivated by the rapid growth of modern signal processing applications and efficient mathematical tools that can handle multidimensional, nonstationary and shifted signals in a unified manner, this paper introduces a new transform, called the biquaternion offset linear canonical Stockwell transform (BiQOLCST). The proposed framework extends existing transform techniques and provides a flexible approach for analyzing complex signal structures. Several important properties of the transform are established, including linearity, anti-linearity, boundedness, shift and modulation properties, orthogonality relations and the reconstruction formula. In addition, Heisenberg, logarithmic and Donoho-Stark uncertainty principles are derived for the proposed transform, highlighting its inherent limits of simultaneous localization in different domains. These results also demonstrate the usefulness of the BiQOLCST in signal representation, analysis and recovery. Furthermore, signal reconstruction is investigated using the Donoho-Stark uncertainty principle, which provides theoretical conditions for the reliable recovery of signals from incomplete information. The potential applications in color image processing and in the analysis of non-stationary signals are explored.\u0000</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01272-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986669","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

Regularization of singular time-dependent Lagrangian systems 奇异时变拉格朗日系统的正则化

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-09-16 DOI: 10.1007/s13324-026-01261-z

M. de León, R. Izquierdo-López, L. Schiavone, P. Soto-Martín

引用次数: 0

Hydrodynamic Green and Robin functions on surfaces with continuous symmetry 流体动力学Green和Robin函数在具有连续对称的表面上

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-09-16 DOI: 10.1007/s13324-026-01270-y

Yuuki Shimizu

{"title":"Hydrodynamic Green and Robin functions on surfaces with continuous symmetry","authors":"Yuuki Shimizu","doi":"10.1007/s13324-026-01270-y","DOIUrl":"10.1007/s13324-026-01270-y","url":null,"abstract":"<div>We derive analytic formulae for the hydrodynamic Green function and the associated Robin function on every orientable surface admitting a hydrodynamic Killing vector field. Explicit formulae are obtained for all fourteen canonical Riemann surfaces, covering both compact and non-compact cases. Moreover, the formulae make explicit how the conformal factor determines the hydrodynamic Green and Robin functions, thereby linking geometric shape data directly to the quantities governing vortex motion. To quantify how a periodic curvature profile affects the velocity of a point vortex, we construct an analytic solution of the Kazdan–Warner equation for the prescribed curvature (kappa (x,y)=kappa _{0}+kappa _{1}cos omega x) on a rectangular torus and use our formulae to obtain an explicit expression for the vortex velocity. The resulting velocity admits two explicit asymptotic regimes: as (kappa _0rightarrow 0), the leading-order term is a single (sin (omega x)) mode whose coefficient vanishes at and changes sign across an explicitly determined critical period; as (|kappa _1|-|kappa _0|rightarrow 0), the same critical period marks a transition in the zero and sign structure of the leading-order profile, whose normalized small- and large-period limits are obtained explicitly. The results supply a unified tool for detailed studies of point vortex dynamics on surfaces with continuous symmetry.</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986461","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

Hydrodynamic Green and Robin functions on surfaces with continuous symmetry 流体动力学Green和Robin函数在具有连续对称的表面上

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-09-16 DOI: 10.1007/s13324-026-01270-y

Yuuki Shimizu

{"title":"Hydrodynamic Green and Robin functions on surfaces with continuous symmetry","authors":"Yuuki Shimizu","doi":"10.1007/s13324-026-01270-y","DOIUrl":"10.1007/s13324-026-01270-y","url":null,"abstract":"<div>We derive analytic formulae for the hydrodynamic Green function and the associated Robin function on every orientable surface admitting a hydrodynamic Killing vector field. Explicit formulae are obtained for all fourteen canonical Riemann surfaces, covering both compact and non-compact cases. Moreover, the formulae make explicit how the conformal factor determines the hydrodynamic Green and Robin functions, thereby linking geometric shape data directly to the quantities governing vortex motion. To quantify how a periodic curvature profile affects the velocity of a point vortex, we construct an analytic solution of the Kazdan–Warner equation for the prescribed curvature (kappa (x,y)=kappa _{0}+kappa _{1}cos omega x) on a rectangular torus and use our formulae to obtain an explicit expression for the vortex velocity. The resulting velocity admits two explicit asymptotic regimes: as (kappa _0rightarrow 0), the leading-order term is a single (sin (omega x)) mode whose coefficient vanishes at and changes sign across an explicitly determined critical period; as (|kappa _1|-|kappa _0|rightarrow 0), the same critical period marks a transition in the zero and sign structure of the leading-order profile, whose normalized small- and large-period limits are obtained explicitly. The results supply a unified tool for detailed studies of point vortex dynamics on surfaces with continuous symmetry.</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986458","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

Regularization of singular time-dependent Lagrangian systems 奇异时变拉格朗日系统的正则化

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-09-16 DOI: 10.1007/s13324-026-01261-z

M. de León, R. Izquierdo-López, L. Schiavone, P. Soto-Martín

引用次数: 0

Elements (functions) that are universal with respect to a minimal system 相对于最小系统来说是通用的元素（函数）

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-09-14 DOI: 10.1007/s13324-026-01268-6

Zhirayr Avetisyan, Martin Grigoryan, Michael Ruzhansky

{"title":"Elements (functions) that are universal with respect to a minimal system","authors":"Zhirayr Avetisyan, Martin Grigoryan, Michael Ruzhansky","doi":"10.1007/s13324-026-01268-6","DOIUrl":"10.1007/s13324-026-01268-6","url":null,"abstract":"<div>We call an element U conditionally universal for a sequential convergence space (mathbf {Omega }) with respect to a minimal system ({varphi _n}_{n=1}^infty ) in a continuously and densely embedded Banach space (mathcal {X}hookrightarrow mathbf {Omega }) if the partial sums of its phase-modified Fourier series is dense in (mathbf {Omega }). We will call the element U almost universal if the change of phases (signs) needs to be performed only on a thin subset of Fourier coefficients. In this paper we prove the existence of an almost universal element under certain assumptions on the system ({varphi _n}_{n=1}^infty ). We will call a function U asymptotically conditionally universal in a space (L^1(mathcal {M})) if the partial sums of its phase-modified Fourier series is dense in (L^1(F_m)) for an ever-growing sequence of subsets (F_msubset mathcal {M}) with asymptotically null complement. Here we prove the existence of such functions U under certain assumptions on the system ({varphi _n}_{n=1}^infty ). Moreover, we show that every integrable function can be slightly modified to yield such a function U. In particular, we establish the existence of almost universal functions for (L^p([0,1])), (pin (0,1)), and asymptotically conditionally universal functions for (L^1([0,1])), with respect to the trigonometric system.</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986338","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