Abstract
This paper treats the exponential linear phase system which consists of eigenfunctions of the discontinuous differential operator. Frame properties of this system are studied in weighted Lebesgue spaces with the variable order of summability.
Highlights
Perturbed system of exponents e i nt n Z plays an important role in the study of spectral properties of discrete differential operators and in the approximation theory
This paper treats the exponential linear phase system which consists of eigenfunctions of the discontinuous differential operator
Frame properties of this system are studied in weighted Lebesgue spaces with the variable order of summability
Summary
Perturbed system of exponents e i nt n Z plays an important role in the study of spectral properties of discrete differential operators and in the approximation theory. There arose a great interest in considering various problems, related to some research fields of mechanics and mathematical physics, in generalized Lebesgue spaces Lp( ) with a variable summability exponent p Application of Fourier method to the problems for partial differential equations in generalized Sobolev classes requires a good knowledge of approximative properties of perturbed exponential systems in generalized Lebesgue spaces. Note that the linear phase sine and cosine systems appear when solving partial differential equations by Fourier method. This work is dedicated to the study of frame properties (atomic decomposition, frameness) of the exponential piecewise linear phase system in generalized weighted Lebesgue space
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