Zobrazeno 1 - 10
of 107
pro vyhledávání: '"Mikhailets, Vladimir A."'
Autor:
Mikhailets, Vladimir, Atlasiuk, Olena
The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the solvability of such
Externí odkaz:
http://arxiv.org/abs/2411.15330
We study the most general class of eigenfunction expansions for abstract normal operators with pure point spectrum in a complex Hilbert space. We find sufficient conditions for such expansions to be unconditionally convergent in spaces with two norms
Externí odkaz:
http://arxiv.org/abs/2312.11247
Autor:
Mikhailets, Vladimir, Atlasiuk, Olena
The aim of the paper is to develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of arbitrary order in Sobolev spaces. Boundary conditions are allowed to be overdetermin
Externí odkaz:
http://arxiv.org/abs/2310.07353
The article studies the convergence of trigonometric Fourier series via a new Tauberian theorem for Ces\`{a}ro summable series in abstract normed spaces. This theorem generalizes some known results of Hardy and Littlewood for number series. We find s
Externí odkaz:
http://arxiv.org/abs/2307.15511
Autor:
Atlasiuk, Olena, Mikhailets, Vladimir
We study linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general (generic) inhomogeneous boundary conditions in Sobolev spaces. We investigate the character of solvability of inhomogeneous bo
Externí odkaz:
http://arxiv.org/abs/2305.00495
Publikováno v:
Ukrainian Mathematical Journal, Vol. 75, No. 1, June, 2023
Systems of linear ordinary differential equations with the most general inhomogeneous boundary conditions in fractional Sobolev spaces on a finite interval are studied. The Fredholm property of such problems in corresponding pairs of Banach spaces is
Externí odkaz:
http://arxiv.org/abs/2211.08039
We introduce and investigate symmetric operators $L_0$ associated in the complex Hilbert space $L^2(\mathbb{R})$ with a formal differential expression \[l[u] :=-(pu')'+qu + i((ru)'+ru') \] under minimal conditions on the regularity of the coefficient
Externí odkaz:
http://arxiv.org/abs/2110.11750
We propose a new viewpoint on Hilbert scales extending them by means of all Hilbert spaces that are interpolation ones between spaces on the scale. We prove that this extension admits an explicit description with the help of $\mathrm{OR}$-varying fun
Externí odkaz:
http://arxiv.org/abs/2102.08089
Autor:
Atlasiuk, Olena, Mikhailets, Vladimir
We consider the most general class of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of an arbitrary order whose solutions and right-hand sides belong to appropriate Sobolev spaces. For parameter-dependent
Externí odkaz:
http://arxiv.org/abs/2005.03494