arXiv subjects

Evgeniy Pustylnik

Publications and source records attributed to Evgeniy Pustylnik.

4 recordsLinked to original sources

arXiv2026

A new approach to interpolation of compact linear operators

We prove an abstract theorem on keeping the compactness property of a linear operator after interpolation in Banach spaces. Our approach consists of two features. Applying the principle "reductio ad absurdum," we obtain a possibility to carry out all proofs only for some specially constructed subspaces of the given spaces, e.g., having a common Schauder basis. As a second feature, we consider in all assertions only embedding operators obtaining the full result just at the end of the paper. No analytical presentation of operators, spaces and interpolation functors is required and the complex method is admissible as a particular case.

math.FA↗

arXiv2021

General Theorem on Interpolation of Compact Operators

We prove an abstract theorem on keeping the compactness property of a linear operator after interpolation in Banach spaces. No analytical presentation of operators, spaces and interpolation functor is required. We use only some little-known properties of compact sets and various facts about bases and basic sequences (with detailed references to the monograph "Bases in Banach spaces", Vol. I-II by I.M. Singer). Therefore the results are applicable to arbitrary spaces and any interpolation functor, including the complex method. The "two-sided" compactness is also mentioned at the end of this paper as a mere corollary.

math.FA↗

arXiv2017

A short proof of solution formulas for the linear differential equations with constant coefficients

The solution of equations from the title is well known since the Euler's time. However, its proof in the case of multiple roots of the characteristic polynomial is rather long and technical and even appearance of the factors $x^m$ looks artificial. A new proof, proposed below, seems not only shorter, but also more comprehensible for the students of any level.

math.CA↗

arXiv2007

Sobolev Inequalities: Symmetrization and Self Improvement via Truncation

We develop a new method to obtain symmetrization inequalities of Sobolev type. Our approach leads to new inequalities and considerable simplification in the theory of embeddings of Sobolev spaces based on rearrangement invariant spaces.

math.FA↗