Characterization of continuous $g$-frames via operators
Copyright policy )Characterization of continuous $g$-frames via operators
In this paper we introduce and show some new notions and results on cg-frames of Hilbert spaces. We define cg-orthonormal bases for a Hilbert space H and verify their properties and relations with cg-frames. Actually, we present that every cg-frame can be represented as a composition of a cg-orthonormal basis and an operator under some conditions. Also, we find for any cg-frame an induced c-frame and study their properties and relations. Moreover, we show that every cg-frame can be written as aggregate of two Parseval cg-frames. In addition, We show each cg-frame as a summation of a cg-orthonormal basis and a cg-Riesz basis.
- Islamic Azad University of Parand Iran (Islamic Republic of)
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Mathematics - Functional Analysis, \(cg\)-orthonormal basis, \(c\)-frame, 42C15, 46C05, Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product), Hilbert space, FOS: Mathematics, General harmonic expansions, frames, \(cg\)-frame, Functional Analysis (math.FA)
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Mathematics - Functional Analysis, \(cg\)-orthonormal basis, \(c\)-frame, 42C15, 46C05, Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product), Hilbert space, FOS: Mathematics, General harmonic expansions, frames, \(cg\)-frame, Functional Analysis (math.FA)
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