Certain mathematical objects appear in a lot of scientific disciplines, like physics, signal processing and, naturally, mathematics. In general setting they can be described as frame multipliers, consisting analysis, multiplication by fixed sequence (called the symbol), and synthesis. this paper we show surprising result about inverse such operators, if any, well new results core concept theory, dual frames. We that for semi-normalized symbols, any invertible multiplier always represented...

Multipliers are operators that combine (frame-like) analysis, a multiplication with fixed sequence, called the symbol, and synthesis. They very interesting mathematical objects also have lot of applications for example in acoustical signal processing. It is known bounded symbols Bessel sequences guarantee unconditional convergence. In this paper we investigate necessary equivalent conditions convergence multipliers. particular show that, under mild conditions, unconditionally convergent...

The duality principle states that a Gabor system is frame if and only the corresponding adjoint Riesz sequence. In general Hilbert spaces without assumption of any particular structure, Casazza, Kutyniok Lammers have introduced so-called R-duals also lead to characterization frames in terms associated sequences; however, it still an open question whether this abstract theory generalization principle. paper we prove modified version leads keeps all attractive properties R-duals. order provide...

In this paper we consider perturbation of several frame-concepts in separable Banach spaces. We determine stability conditions with sharp bounds and discuss the necessity some them. Further, investigate equivalence between conditions. particular, a result for tight frames Hilbert spaces is obtained.

Abstract In this paper, we study the problem of recovering a signal from frame coefficients with erasures. Suppose that erased are indexed by finite set E . Starting $$(x_n)_{n=1}^\infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mi>∞</mml:mi> </mml:msubsup> </mml:math> and its arbitrary dual...

The main purpose of the paper is to give a characterization all compactly supported dual windows Gabor frame. As an application, we consider iterative procedure for approximation canonical window via on every step. In particular, allows have from certain modulation spaces or Schwartz space.

X d -frames for Banach spaces are generalization of Hilbert frames. In this paper we extend the concepts frame operator and canonical dual to case -frames. For a given -frame {g i } space define an map𝕊 : → X* determine conditions, which imply that 𝕊 is invertible family {𝕊 -1 g [Formula: see text]-frame such f = ∑g (f)𝕊 every ∈ ∑g(𝕊 )g X*. If X, then ℓ 2 map gives S coincides with }.

In this paper we investigate the possibility of unconditional convergence and invertibility multipliers $M_{m,Φ,Ψ}$ depending on properties sequences $Ψ$,$Φ$ $m$. We characterize a complete set conditions for multipliers, collect those results in tables. either prove that is not possible, one or both these are always case given parameters, give examples feasible combinations. full list all conditions.

It is well known that a frame {gi } for Hilbert space ℋ allows every element f∈ℋ to be represented as f=∑ ⟨ f, f i ⟩ g =∑ via the elements and dual {fi }, ∈ℋ. For some generalizations of frames Banach spaces (Banach frames, p-frames), such representations are not always possible. given sequence with in X* X, we discuss p-frame condition validity series expansions form g=∑ d appropriate coefficients {di also reconstruction (f) , f∈X, g(f ) g∈X*, ∈X. In particular, show w.r.t. ℓ p leads...

In this paper we consider series expansions via a frame and non-frame the possibilities for interchange of two sequences, both in Hilbert Banach space setting. First give characterization frame-related concepts spaces (atomic decompositions, frames, $X_d$-Riesz bases, $X_d$-frames, $X_d$-Bessel sequences satisfying lower $X_d$-frame condition). We also determine necessary sufficient conditions operators to preserve type listed above. Then discuss differences relationships between its dual...