Related papers: Nigel Kalton and complex interpolation of compact …
The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued…
Let $\mathcal{H}$ be a separable complex Hilbert space. A conjugate-linear map $C:\mathcal{H}\to \mathcal{H}$ is called a conjugation if it is an involutive isometry. In this paper, we focus on the following interpolation problems: Let…
We examine interpolatory model reduction methods that are well-suited for treating large scale port-Hamiltonian differential-algebraic systems in a way that is able to preserve and indeed, take advantage of the underlying structural…
Tensor interpolation is an essential step for tensor data analysis in various fields of application and scientific disciplines. In the present work, novel interpolation schemes for general, i.e., symmetric or non-symmetric, invertible…
Transformations in the field of computer graphics and geometry are one of the most important concepts for efficient manipulation and control of objects in 2-dimensional and 3-dimensional space. Transformations take many forms each with…
Conformal Regge theory predicts the existence of analytically continued CFT data for complex spin. How could this work when there are so many more operators with large spin compared to small spin? Using planar N=4 SYM as a testground we…
This paper presents a new approach of constructing $\alpha$-fractal interpolation functions (FIFs) using neural network operators, integrating concepts from approximation theory. Initially, we construct $\alpha$-fractals utilizing neural…
The monograph contains the detailed exposition of the results obtained by the author during the last several years. In particular it contains an improvement of the well known Calderon - Ryff interpolation theorem and description of…
The study is made of the problem of multiple interpolation on an infinite nodes set by the sums of absolutely convergent series of exponentials whose exponents are from a given set. For entire function conditions on nodes and exponents are…
Interpolation for scattered data is a classical problem in numerical analysis, with a long history of theoretical and practical contributions. Recent advances have utilized deep neural networks to construct interpolators, exhibiting…
The classical $L^2$ estimate for the $\overline{\partial}$ operators is a basic tool in complex analysis of several variables. Naturally, it is expected to extend this estimate to infinite dimensional complex analysis, but this is a…
We study operators on the Kalton-Peck Banach space $Z_2$ from various points of view: matrix representations, examples, spectral properties and operator ideals. For example, we prove that there are non-compact, strictly singular operators…
Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial…
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…
This paper investigates some univariate and bivariate constrained interpolation problems using rational quartic fractal interpolation functions, which has been submitted long back in a reputed journal and revised as per the journal…
Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is to find a point in the intersection of the fixed point sets of these operators. Instances of the problem have numerous…
When G is a region in the complex plane, compact composition operators on the uniform algebra of bounded analytic functions on G and the spectra of these operators were described by D. Swanton, Compact composition operators on B(D), Proc.…
Interpolation theory for complex polynomials is well understood. In the non-commutative quaternionic setting, the polynomials can be evaluated "on the left" and "on the right". If the interpolation problem involves interpolation conditions…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…