248 research outputs found
Invariance of Fr\'echet Frames under Perturbation
Motivating the perturbations of frames in Hilbert and Banach spaces, in this
paper we introduce the invariance of Fr\'echet frames under perturbation. Also
we show that for any Fr\'echet spaces, there is a Fr\'echet frame and any
element has a series expansion.Comment: 10 page
Controlled G-Frames and Their G-Multipliers in Hilbert spaces
Multipliers have been recently introduced by P. Balazs as operators for
Bessel sequences and frames in Hilbert spaces. These are operators that combine
(frame-like) analysis, a multiplication with a fixed sequence (called the
symbol) and synthesis. Weighted and controlled frames have been introduced to
improve the numerical efficiency of iterative algorithms for inverting the
frame operator Also g-frames are the most popular generalization of frames that
include almost all of the frame extensions. In this manuscript the concept of
the controlled g-frames will be defined and we will show that controlled
g-frames are equivalent to g-frames and so the controlled operators C and C0
can be used as preconditions in applications. Also the multiplier operator for
this family of operators will be introduced and some of its properties will be
shown.Comment: 15 page
Finite equal norm Parseval Wavelet Frames over Prime Fields
In the framework of wave packet analysis, finite wavelet systems are
particular classes of finite wave packet systems. In this paper, using a
scaling matrix on a permuted version of the discrete Fourier transform (DFT) of
system generator, we derive a locally-scaled version of the DFT of system
genarator and obtain a finite equal-norm Parseval wavelet frame over prime
fields. We also give a characterization of all multiplicative subgroups of the
cyclic multiplicative group, for which the associated wavelet systems form
frames. Finally, we present some concrete examples as applications of our
results.Comment: arXiv admin note: text overlap with arXiv:1703.0501
A Constructive Approach to the Finite Wavelet Frames over Prime Fields
In this article, we present a constructive method for computing the frame
coefficients of finite wavelet frames over prime fields using tools from
computational harmonic analysis and group theory.Comment: 11 page
On Controlled Frames in Hilbert -modules
In this paper, we introduce controlled frames in Hilbert -modules and we
show that they share many useful properties with their corresponding notions in
Hilbert space. Next, we give a characterization of controlled frames in Hilbert
-module. Also multiplier operators for controlled frames in Hilbert
-modules will be defined and some of its properties will be shown.
Finally, we investigate weighted frames in Hilbert -modules and verify
their relations to controlled frames and multiplier operators
Redundancy of Fusion frames in Hilbert Spaces
Upon improving and extending the concept of redundancy of frames, we
introduce the notion of redundancy of fusion frames, which is concerned with
the properties of lower and upper redundancies. These properties are achieved
by considering the minimum and maximum values of the redundancy function which
is defined from the unit sphere of the Hilbert space into the positive real
numbers. In addition, we study the relationship between redundancy of frames
(fusion frames) and dual frames (dual fusion frames). Moreover, we indicate
some results about excess of fusion frames. We state the relationship between
redundancy of local frames and fusion frames in a particular case. Furthermore,
some examples are also given
Dual pair and Approximate dual for continuous frames in Hilbert spaces
In this manuscript, the concept of dual and approximate dual for continuous
frames in Hilbert spaces will be introduced. Some of its properties will be
studied. Also, the relations between two continuous Riesz bases in Hilbert
spaces will be clarified through examples.Comment: 18 page
Controlled K-frames in Hilbert Spaces
K-frames were recently introduced by L. G\v{a}vruta in Hilbert spaces to
study atomic systems with respect to bounded linear operator. Also controlled
frames have been recently introduced by P. Balazs in Hilbert spaces to improve
the numerical efficiency of interactive algorithms for inverting the frame
operator. In this manuscript, we will define the concept of the controlled
K-frames and will show that controlled K-frames are equivalent to K-frames and
so the controlled operator C can be used as preconditions in applications.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1602.0398
The Effect of Perturbations of Frames and Fusion Frames on Their Redundancies
An interesting question about the perturbed sequences is: when do they
inherit the properties of the original one? An elegant relation between frames
(fusion frames) and their perturbations is the relation of their redundancies.
In this paper, we investigate these relationships. Also, we express the
redundancy of frames (fusion frames) in terms of the cosine angle between some
subspaces.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1509.04160,
arXiv:0910.5904 by other author
Adjoint of Pair Frames
The concept of (p,q)-pair frames is generalized to (l,l^*)-pair frames.
Adjoint (conjugate) of a pair frames for dual space of a Banach space is
introduced and some conditions for the existence of adjoint (conjugate) of pair
frames are presented
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