It is intended to find the best representation of high-dimensional functions or multivariate data in L2(W) with fewest number of terms, each of them is a combination of one-variable function. A system of nonlinear int...
IN ref. [1] for the subspaces of Hilbert space H the concept of equivalence and a generalizeddimension are introduced. Note that in refs. [2, 3] many results are true only in the separablespace. We introduce a concept...
The study of the reliability of operator’s diagnosis and decision-making during abnormal events with HCR model has been introduced. A new approach has been proposed by the authors to deal with the classification of H...
SINCE Michael (1952) published the first book about topological algebras, it has become abranch of functional analysis. Applications of topological algebras have been found in complexanalysis of several variables, dif...
QUANTIZED radiation fields exhibiting nonclassical properties have been of great theoretical andexperimental interest in the last two decades. It is shown that various nonclassical states suchas squeezed state and Sch...
LET A be a closed operator on a Banach space X, and C~∞ (A)=∩_n~∞=1,D(A^n). The C~∞ vec-tor x is an entire vector for A if sum from n=0 to ∞ (t^n)/(n!)||A^n x||<∞ (1)for all t>0. We will write ε(A) for th...
LET Bn be the unit ball of Cn. The n-dimensional vector space over the complex field C, Sn=(?)Bn is the boundary of Bn. We use σ to denote the unique rotation-...
LET H be an infinite-dimensional complex Hilbert space with inner product <·,·> and B(H) the von Neumann algebra of all bounded linear operators on H. For T∈B(H), σ(T), as usual, will denote the spectrum of ...
Soria and Weiss extended a Stein’s result,the boundedness of singular integral op-erators on the weighted spaces L^p(w) with power weights w, to more general cases wheresingular integral operators were replaced by su...
A (bounded finear) operator T on a (separable, infinite, dimensional, complex) Hilbert space (?) is said to be irreducible if there is no nontrivial (orthogonal) projection P commuting with T. In Ref. [1], Halmos prov...