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On basicity of eigenfunctions of one discontinuous differential operator in Banach function spaces
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This article deals with the basicity properties of the eigenfunctions
system of a second-order discontinuous differential operator containing
spectral parameters at boundary conditions in Banach function spaces.
Investigations are divided into two groups depending on being a
rearrangement-invariant space. By imposing some conditions on the Boyd
indices of rearrangement-invariant Banach function spaces, we prove some
important properties of the basicity of the eigenfunctions system of the
spectral problem in suitable separable subspaces of these spaces. These
properties are valid in Lebesgue, grand-Lebesgue, Orlics, and
Marcinkiewicz. Also, results regarding the basicity of the system of
eigenfunctions in non-rearrangement invariant spaces that are a direct
sum of rearrangement-invariant spaces with different finite Boyd indices
have been obtained. The discontinuity of the differential operator makes
it possible to examine the basicity properties of the system of
eigenfunctions in the direct sum space of spaces with finite Boyd
indices.
Title: On basicity of eigenfunctions of one discontinuous differential operator in Banach function spaces
Description:
This article deals with the basicity properties of the eigenfunctions
system of a second-order discontinuous differential operator containing
spectral parameters at boundary conditions in Banach function spaces.
Investigations are divided into two groups depending on being a
rearrangement-invariant space.
By imposing some conditions on the Boyd
indices of rearrangement-invariant Banach function spaces, we prove some
important properties of the basicity of the eigenfunctions system of the
spectral problem in suitable separable subspaces of these spaces.
These
properties are valid in Lebesgue, grand-Lebesgue, Orlics, and
Marcinkiewicz.
Also, results regarding the basicity of the system of
eigenfunctions in non-rearrangement invariant spaces that are a direct
sum of rearrangement-invariant spaces with different finite Boyd indices
have been obtained.
The discontinuity of the differential operator makes
it possible to examine the basicity properties of the system of
eigenfunctions in the direct sum space of spaces with finite Boyd
indices.
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