Isaev, K. P.
Published in
Russian Mathematics

We introduce a normed space of functions, holomorphic in a bounded convex domain. Its elements are infinitely differentiable up to the boundary, and all their derivatives satisfy estimates specified by a convex sequence of positive numbers. We consider its largest linear subspace that is invariant with respect to the operator of differentiation and...

Čapka, Ferdinand

Práca sa zaoberá problematikou variačných nerovníc, minimalizáciou energetických funkcionálov, pomerne hlbokou abstraktnou teóriou funkcionálnej analýzy, ktorá nám umožní vybudovať netriviálny dôkaz vety, ktorá zaručuje existenciu riešenia variačnej nerovnice. Aplikačný aspekt práce je zameraný na rôzne numerické experimenty. V práci využívam aj al...

Mishin, S. N.
Published in
Russian Mathematics

We consider a general method of solving equations whose left-hand side is a series by powers of a linear continuous operator acting in a locally convex space. Obtained solutions are given by operator series by powers of the same operator as the left-hand side of the equation. The research is realized by means of characteristics (of order and type) ...

Eskandarian, Zohreh
Published in
Lobachevskii Journal of Mathematics

We consider linear normed spaces of measurable functions dominated by positive measurable function powered by real positive parameter. Also, we consider its dual and predual, and we propose a method for constructing a limit spaces of these functional spaces taken by power parameter. We prove that these limit spaces are (LF)-spaces and also prove th...

Man’ko, S. N.
Published in
Russian Mathematics

This work is devoted to solving some classes of operator equations, based on the solution of auxiliary one-parameter family of equations, which is obtained fromthe original operator equation by formal replacement of the operator of the integrated parameter. Solutions are vector-valued functions represented by power series or integral. We investigat...

Mishin, S. N.
Published in
Mathematical Notes

The well-known Lagrange method for linear inhomogeneous differential equations is generalized to the case of second-order equations with constant operator coefficients in locally convex spaces. The solutions are expressed in terms of uniformly convergent functional vector-valued series generated by a pair of elements of a locally convex space. Suff...

Kostić, M. Pilipović, S. Velinov, D.
Published in
Siberian Mathematical Journal

The main purpose of this paper is to study C-distribution semigroups and C-ultradistribution semigroups in the setting of sequentially complete locally convex spaces. We provide a few important theoretical novelties in this field and some interesting examples. Under consideration are stationary dense operators in a sequentially complete locally con...

Mishin, S. N.
Published in
Russian Mathematics

We describe a general method that allows us to find solutions to homogeneous differential-operator equations with variable coefficients by means of continuous vector-valued functions. The “homogeneity” is not interpreted as the triviality of the right-hand side of an equation. It is understood in the sense that the left-hand side of an equation is ...

Novikov, A. A. Eskandarian, Z.
Published in
Russian Mathematics

We prove that a measurable function f is bounded and invertible if and only if there exist at least two equivalent norms by order unit spaces with order unities fα and fβ with α > β > 0. We show that it is natural to understand the limit of ordered vector spaces with order unities fα (α approaches to infinity) as a direct sum of one inductive and o...

Mishin, S. N.
Published in
Mathematical Notes

In the paper, the invariance property of characteristics (the order and type) of an operator and of a sequence of operators with respect to a topological isomorphism is proved. These characteristics give precise upper and lower bounds for the expressions ‖An(x)‖p and enable one to state and solve problems of operator theory in locally convex spaces...