Papers by Morteza Rahmani
Iranian Journal of Science and Technology, Transactions A: Science, 2022
In this paper we study some new properties of c-K-g-frames in a Hilbert space H. We study duals o... more In this paper we study some new properties of c-K-g-frames in a Hilbert space H. We study duals of c-K-g-frames and give some characterizations of c-K-g-frames and their duals. Also, we verify the relationships between c-K-g-frames and atomic cg-systems. Precisely, we show that these two concepts are equivalent. Finally, we find some new atomic cg-systems from given ones.
In this paper we introduce and prove some new concepts and results on c-frames for Hilbert spaces... more In this paper we introduce and prove some new concepts and results on c-frames for Hilbert spaces. We define c-Riesz bases for a Hilbert space H and state some results to characterize them. Then, we give necessary and sufficient conditions on c-Bessel mappings f and g and operators L1, L2 on H so that L1f+ L2g is a c-frame for H. This allows us to construct a large number of new cframes by existing c-frames. Also, we define orthonormal mappings for H and we specify a necessary and sufficient condition to represent a c-frame as a linear combination of two orthonormal mappings. Moreover, we show that every c-frame can be written as a (multiple of a) sum of two Parseval c-frames; it can also be written as a (multiple of a) sum of an orthonormal mapping and a c-Riesz basis.
arXiv: Functional Analysis, 2018
In this paper we introduce and show some new notions and results on cg-frames of Hilbert spaces. ... more 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 traits and relations with cg-frames. Actually, we present that every cg-frame can be present as a composition of a cg-orthonormal basis and an operator under some conditions. Also, we give 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, each cg-frame can be shown as a summation of a cg-orthonormal basis and a cg-Riesz basis.
Proceedings of the Institute of Mathematics and Mechanics,National Academy of Sciences of Azerbaijan, 2020
In this paper we introduce and show some new notions and results on cg-frames of Hilbert spaces. ... more 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 cgframes. 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 addition of two Parseval cg-frames. In addition, we show each cg-frame as a sum of a cg-orthonormal basis and a cg-Riesz basis.
International Mathematical Forum, 2013
Journal of Inequalities and Applications, 2012
Involve, a Journal of Mathematics, 2012
Using the concepts of Bochner measurability and Bochner space, we introduce a continuous version ... more Using the concepts of Bochner measurability and Bochner space, we introduce a continuous version of (p, Y)-operator frames for a Banach space. We also define independent Bochner (p, Y)-operator frames for a Banach space and discuss some properties of Bochner (p, Y)-operator frames.
In this paper we introduce and prove some new concepts and results on
c-frames for Hilbert spaces... more In this paper we introduce and prove some new concepts and results on
c-frames for Hilbert spaces. We define c-Riesz bases for a Hilbert space H and
state some results to characterize them. Then, we give necessary and sufficient
conditions on c-Bessel mappings f and g and operators L1;L2 on H so that L1f+
L2g is a c-frame for H. This allows us to construct a large number of new c-
frames by existing c-frames. Also, we define orthonormal mappings for H and
we specify a necessary and sufficient condition to represent a c-frame as a linear
combination of two orthonormal mappings. Moreover, we show that every c-frame
can be written as a (multiple of a) sum of two Parseval c-frames; it can also be
written as a (multiple of a) sum of an orthonormal mapping and a c-Riesz basis.
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Papers by Morteza Rahmani
c-frames for Hilbert spaces. We define c-Riesz bases for a Hilbert space H and
state some results to characterize them. Then, we give necessary and sufficient
conditions on c-Bessel mappings f and g and operators L1;L2 on H so that L1f+
L2g is a c-frame for H. This allows us to construct a large number of new c-
frames by existing c-frames. Also, we define orthonormal mappings for H and
we specify a necessary and sufficient condition to represent a c-frame as a linear
combination of two orthonormal mappings. Moreover, we show that every c-frame
can be written as a (multiple of a) sum of two Parseval c-frames; it can also be
written as a (multiple of a) sum of an orthonormal mapping and a c-Riesz basis.
c-frames for Hilbert spaces. We define c-Riesz bases for a Hilbert space H and
state some results to characterize them. Then, we give necessary and sufficient
conditions on c-Bessel mappings f and g and operators L1;L2 on H so that L1f+
L2g is a c-frame for H. This allows us to construct a large number of new c-
frames by existing c-frames. Also, we define orthonormal mappings for H and
we specify a necessary and sufficient condition to represent a c-frame as a linear
combination of two orthonormal mappings. Moreover, we show that every c-frame
can be written as a (multiple of a) sum of two Parseval c-frames; it can also be
written as a (multiple of a) sum of an orthonormal mapping and a c-Riesz basis.