Related papers: Complex Iterations and Bounded Analytic Hyper-oper…
In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. \ We first establish a criterion on the coprime-ness of two singular inner functions and…
The object of this paper is to investigate the certain results involving Bateman's matrix polynomials for integral index. We obtain some properties, integral representation and recurrence relations for hypergeometric matrix function. We…
The paper outlines the principles of construction of a broad class of hierarchical aggregation algorithms of cluster analysis, essentially based on minimum distance mergers, which are derived from the general bi-partial objective function.…
In the article integer divisibility properties and related prime factors natural number representation concepts have been defined over the whole infinite hyperoperation hierarchy. The definitions have been made across and above of unique…
Fold functions are a general mechanism for computing over recursive data structures. First-order folds compute results bottom-up. With higher-order folds, computations that inherit attributes from above can also be expressed. In this paper,…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
We study the boundedness problem for maximal operators in 3-dimensional Euclidean space associated to hypersurfaces given as the graph of $c+f$, where $f$ is a mixed homogeneous function which is smooth away from the origin and $c$ is a…
We present a dimension-incremental method for function approximation in bounded orthonormal product bases to learn the solutions of various differential equations. Therefore, we decompose the source function of the differential equation…
Expansion of higher transcendental functions in a small parameter are needed in many areas of science. For certain classes of functions this can be achieved by algebraic means. These algebraic tools are based on nested sums and can be…
We study non-autonomous conformal iterated function systems, with finite or countably infinite alphabet alike. These differ from the usual (autonomous) iterated function systems in that the contractions applied at each step in time are…
We develop the theory of integrable operators $\mathcal{K}$ acting on a domain of the complex plane with smooth boundary in analogy with the theory of integrable operators acting on contours of the complex plane. We show how the resolvent…
We study several natural multiplicity questions that arise in the context of the Birman-Schwinger principle applied to non-self-adjoint operators. In particular, we re-prove (and extend) a recent result by Latushkin and Sukhtyaev by…
We develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion…
We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…
We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard-Marchaud fractional derivative, is also considered. The objective is to represent these…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
We present a dimension-incremental algorithm for the nonlinear approximation of high-dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to detect a suitable truncation of the basis expansion of the…