نتایج جستجو برای: Singleton g-orthonormal basis

تعداد نتایج: 813402  

We introduce a new g-frame (singleton g-frame), g-orthonormal basis and g-Riesz basis and study corresponding notions in some other generalizations of frames.Also, we investigate duality  for some kinds of g-frames. Finally, we illustrate an example which provides a  suitable translation from discrete frames to Sun's g-frames.

In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual fra...

Journal: :sahand communications in mathematical analysis 2015
mehdi rashidi-kouchi akbar nazari

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

Journal: :Adv. Comput. Math. 2003
Youming Liu Yang Wang

There have been extensive studies on non-uniform Gabor bases and frames in recent years. But interestingly there have not been a single example of a compactly supported orthonormal Gabor basis in which either the frequency set or the translation set is non-uniform. Nor has there been an example in which the modulus of the generating function is not a characteristic function of a set. In this pa...

2011
Abdolaziz Abdollahi Elham Rahimi

In this paper we show that every g-frame for a Hilbert space H can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. We also show that every g-frame can be written as a sum of two tight g-frames with g-frame bounds one or a sum of a g-orthonormal basis and a g-Riesz basis for H . We further give necessary and sufficient conditions on g-Besse...

S. S. Karimizad

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

Journal: :journal of linear and topological algebra (jlta) 0
s s. karimizad department of mathematics, faculty of science, islamic azad university, central tehran branch, tehran, iran

g-frames in hilbert spaces are a redundant set of operators which yield a repre-sentation for each vector in the space. in this paper we investigate the connection betweeng-frames, g-orthonormal bases and g-riesz bases. we show that a family of bounded opera-tors is a g-bessel sequences if and only if the gram matrix associated to its de nes a boundedoperator.

Journal: :journal of linear and topological algebra (jlta) 0
f aboutorabi goudarzi department of mathematics, faculty of science, central tehran branch, islamic azad university, tehran, iran. m. s asgari department of mathematics, faculty of science, central tehran branch, islamic azad university, tehran, iran.

in this paper we investigate a new notion of bases in hilbert spaces and similarto fusion frame theory we introduce fusion bases theory in hilbert spaces. we also introducea new de nition of fusion dual sequence associated with a fusion basis and show that theoperators of a fusion dual sequence are continuous projections. next we de ne the fusionbiorthogonal sequence, bessel fusion basis, hilbe...

2004
DEGUANG HAN YANG WANG

For an arbitrary full rank lattice Λ in R and a function g ∈ L(R) the Gabor (or Weyl-Heisenberg) system is G(Λ, g) := {eg(x − κ) ̨ ̨ (κ, `) ∈ Λ}. It is well-known that a necessary condition for G(Λ, g) to be an orthonormal basis for L(R) is that the density of Λ has D(Λ) = 1. However, except for symplectic lattices it remains an unsolved question whether D(Λ) = 1 is sufficient for the existence o...

Journal: :journal of sciences, islamic republic of iran 2013
a.a. arefijamaal r.a. kamyabi gol r. raisi tousi n. tavallaei

this paper deals with continuous frames and continuous riesz bases. we introduce continuous riesz bases and give some equivalent conditions for a continuous frame to be a continuous riesz basis. it is certainly possible for a continuous frame to have only one dual. such a continuous frame is called a riesz-type frame [13]. we show that a continuous frame is riesz-type if and only if it is a con...

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