TY - JOUR

T1 - Fundamental Properties of Fractional Powers of Unbounded Operators in Banach Spaces

AU - Belonosov, V. S.

AU - Shvets, A. G.

N1 - The work was carried out within the framework of the state assignment of the Sobolev Institute of Mathematics SB RAS (project no. FWNF-2022-0008).

PY - 2025/1/14

Y1 - 2025/1/14

N2 - Abstract: We extend the classical theory of operator-valued analytic functions to a wide class oflinear unbounded operators defined in Banach spaces on sets that need not be everywhere dense.We also describe properties of fractional powers of these operators. The class under considerationincludes the Sturm–Liouville differential operator with homogeneous Dirichlet boundaryconditions that acts in a space of continuous functions on a bounded interval.

AB - Abstract: We extend the classical theory of operator-valued analytic functions to a wide class oflinear unbounded operators defined in Banach spaces on sets that need not be everywhere dense.We also describe properties of fractional powers of these operators. The class under considerationincludes the Sturm–Liouville differential operator with homogeneous Dirichlet boundaryconditions that acts in a space of continuous functions on a bounded interval.

KW - abstract Mathieu–Hill equations

KW - fractional powers

KW - operator exponentials

KW - parametric resonance

KW - reduction to standard form

UR - https://www.mendeley.com/catalogue/08cbe1f1-4029-3bfc-88cf-7582304c1a2a/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85217413886&origin=inward&txGid=dea0b3261f7d1dde7224fa3d5a64d0e6

U2 - 10.1134/S1055134424040023

DO - 10.1134/S1055134424040023

M3 - Article

VL - 34

SP - 268

EP - 272

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 4

ER -