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In this paper, we will discuss the use of a Sampling Method to reconstruct impenetrable inclusions from Electrostatic Cauchy data. We consider the case of a perfectly conducting and impedance inclusion. In either case, we show that the…

Analysis of PDEs · Mathematics 2021-02-10 Isaac Harris

Matrix-valued Cauchy bi-orthogonal polynomials were proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in four-term recurrence relation for matrix-valued Cauchy bi-orthogonal polynomials…

Mathematical Physics · Physics 2023-01-02 Shi-Hao Li , Ying Shi , Guo-Fu Yu , Jun-Xiao Zhao

We present a semi-Lagrangian method for the numerical resolution of Vlasov-type equations on multi-patch meshes. Following N. Crouseilles et al. [A parallel Vlasov solver based on local cubic spline interpolation on patches. Journal of…

Numerical Analysis · Mathematics 2026-01-26 Pauline Vidal , Emily Bourne , Virginie Grandgirard , Michel Mehrenberger , Eric Sonnendrücker

In this paper we study a family of non-classical Jacobi polynomials with varying parameters of the form $\alpha_n=n+1/2$ and $\beta_n=-n-1/2$. We obtain global asymptotics for these polynomials, and use this to establish results on the…

Classical Analysis and ODEs · Mathematics 2025-03-21 John Lopez Santander , Kenneth D. T-R McLaughlin , Victor H. Moll

We apply the original semiclassical approach to the kinetic ionization equation with the nonlocal cubic nonlinearity in order to construct the family of its asymptotic solutions. The approach proposed relies on an auxiliary dynamical system…

Mathematical Physics · Physics 2023-01-05 Alexander V. Shapovalov , Anton E. Kulagin , Sergei A. Siniukov

We formalize a technique for embedding Riemann sufraces properly into \C^2, and we generalize all known embedding results to allow interpolation on prescribed discrete sequences.

Complex Variables · Mathematics 2007-05-23 Frank Kutzschebauch , Erik Low , Erlend Fornaess Wold

We introduce a class of central symmetric infinitely divisible probability measures on compact Lie groups by lifting the characteristic exponent from the real line via the Casimir operator. The class includes Gauss, Laplace and stable-type…

Probability · Mathematics 2012-02-14 David Applebaum

In this work, we propose a new approach called ``stationary reduction method based on nonisospectral deformation of orthogonal polynomials" for deriving discrete Painlev\'{e}-type (d-P-type) equations. We apply this approach to…

Exactly Solvable and Integrable Systems · Physics 2025-09-18 Xiao-Lu Yue , Xiang-Ke Chang , Xing-Biao Hu

We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ($L^\infty$) coefficients. Our method does not rely on concepts of ergodicity or…

Numerical Analysis · Mathematics 2019-02-20 Houman Owhadi , Lei Zhang , Leonid Berlyand

Our two principle goals are generalizations of the commutant lifting theorem and the Nevanlinna-Pick interpolation theorem to the context of Hardy algebras built from $W^*$-correspondences endowed with a sequence of weights. These theorems…

Operator Algebras · Mathematics 2016-08-18 Jennifer R Good

We present an operator version of the Callebaut inequality involving the interpolation paths and apply it to the weighted operator geometric means. We also establish a matrix version of the Callebaut inequality and as a consequence obtain…

Functional Analysis · Mathematics 2021-07-23 M. S. Moslehian , J. S. Matharu , J. S. Aujla

Sharp $L^\infty$ estimates are obtained for general classes of fully non-linear PDE's on non-K\"ahler manifolds, complementing the theory developed earlier by the authors in joint work with F. Tong for the K\"ahler case. The key idea is…

Differential Geometry · Mathematics 2023-03-01 Bin Guo , Duong H. Phong

We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the…

Complex Variables · Mathematics 2015-10-05 Adam Coffman , Yifei Pan , Yuan Zhang

Using Gabor analysis, we give a complete characterization of all lattice sampling and interpolating sequences in the Fock space of polyanalytic functions, displaying a "Nyquist rate" which increases with $n$, the degree of polyanaliticity…

Functional Analysis · Mathematics 2009-12-02 Luis Daniel Abreu

We present a novel hybrid numerical-asymptotic boundary element method for high frequency acoustic and electromagnetic scattering by penetrable (dielectric) convex polygons. Our method is based on a standard reformulation of the associated…

Numerical Analysis · Mathematics 2017-12-15 Samuel P. Groth , David P. Hewett , Stephen Langdon

Based on the Riemann-Liouville derivatives with respect to functions taking values in the set of hyperbolic numbers, we consider a novel bicomplex proportional fractional $(\vartheta,\varphi)-$weighted Cauchy-Riemann operator, involving…

Complex Variables · Mathematics 2023-08-31 José Oscar González-Cervantes , Juan Adrián Ramírez-Belman , Juan Bory-Reyes

In this paper, we continue the development of a fundament of discrete octonionic analysis that is associated to the discrete first order Cauchy-Riemann operator acting on octonions. In particular, we establish a discrete octonionic version…

Complex Variables · Mathematics 2023-05-09 Rolf Sören Kraußhar , Dmitrii Legatiuk

We prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian in polygons with analytic right-hand side. We localize the problem through the Caffarelli-Silvestre extension and study the…

Analysis of PDEs · Mathematics 2023-11-27 Markus Faustmann , Carlo Marcati , Jens Markus Melenk , Christoph Schwab

Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…

Numerical Analysis · Mathematics 2024-03-28 P. N. Vabishchevich

We study the Cauchy problem for a nonlinear damped wave equation. Under suitable assumptions for the nonlinearity and the initial data, we obtain the global solution which satisfies weighted $L^1$ and $L^\infty$ estimates. Furthermore, we…

Analysis of PDEs · Mathematics 2017-12-01 Tatsuki Kawakami , Hiroshi Takeda