Related papers: Shape Holomorphy of Boundary Integral Operators on…
We prove error bounds for operator surrogates of solution operators for partial differential and boundary integral equations on families of domains which are diffeomorphic to one common reference (or latent) domain $D_{ref}$. The pullback…
We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential…
The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…
The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the…
Algebraic approach to the integrability condition called shape invariance is briefly reviewed. Various applications of shape-invariance available in the literature are listed. A class of shape-invariant bound-state problems which represent…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…
The classical results about the boundary values of holomorphic or harmonic functions on a domain $D$ state that under additional integrability assumptions these functions have limits along specific sets approaching boundary. The proofs of…
Let X be a complex analytic space. A short analytic arc is a holomorphic map of the closed unit disc to X such that only the origin is mapped to a singular point. In contrast with the space of formal arcs studied by Nash, the moduli space…
We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of holomorphic functions into a particular type of spaces of functions determined by the growth of the functions, or the growth…
Necessary and sufficient geometric conditions are given for domains with regular boundary points and edges to be domains of holomorphy provided the remainder boundary subset is of zero Hausdorff 1-codimensional measure.
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
We investigate how IR modifications of the bulk geometry reshape long-range multipartite entanglement on the boundary in holography. We modify the IR geometries in two opposite directions: spherical modifications that enhance long-range…
We investigate the relationship between supersymmetric gauge theories with moduli spaces and matrix models. Particular attention is given to situations where the moduli space gets quantum corrected. These corrections are controlled by…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…
Shape calculus concerns the calculation of directional derivatives of some quantity of interest, typically expressed as an integral. This article introduces a type of shape calculus based on localized dilation of boundary faces through…
For an embedded conformal hypersurface with boundary, we construct critical order local invariants and their canonically associated differential operators. These are obtained holographically in a construction that uses a singular Yamabe…
This paper is concerned with the boundary integral equation method for solving the exterior Neumann boundary value problem of dynamic poroelasticity in two dimensions. The main contribution of this work consists of two aspescts: the…
In this article, we study the analytic properties of the multiple polylogarithms in the $s$-aspect. Although the domain of absolute convergence of the series defining the multiple polylogarithms is well-known, the study towards a larger…
We study analysis over infinite dimensional manifolds consisted by sequences of almost K\"ahler manifolds. In particular we develop moduli theory of pseudo holomorphic curves into the spaces with high symmetry. As applications, we study…