Shawgy Hussein - Academia.edu (original) (raw)
Papers by Shawgy Hussein
The description of the spectra tiling properties and Gabor orthonormal bases generated by the uni... more The description of the spectra tiling properties and Gabor orthonormal bases generated by the unit cubes and of the exponential for the 𝑛-cube are characterized. In addition the uniformity of non-uniform Gabor bases, atomic characterizations of modulation spaces through Gabor representations with Weyl-Heisenberg frames on Hilbert space, slanted matrices and Banach frames are clearly improved. We obtain the density, stability, generated characteristic function and Hamiltonian deformations of Gabor frames. We find estimates for vector –valued Gabor frames of Hermite functions plus periodic subsets of the real line. The Gabor frame sets for subspace with totally positive functions and deformation of Gabor systems are considered.
For describing the space (C[0,1],X) , where X is a Banach space, of absolutely summing operators ... more For describing the space (C[0,1],X) , where X is a Banach space, of absolutely summing operators from C[0, 1] to X in terms of the space X itself, we construct a tree space l1 (X) on X. It consists of special trees in X which we call two-trunk trees. We show that P(C[0,1],X)is isometrically isomorphic to l1 (X). As an application on [19], we characterize the bounded approximation property (BAP) and the weak BAP in terms of X-valued square sequence spaces.
Global Journal of Science Frontier Research, 2019
In this paper, apply an established transference principle to obtain the boundedness of certain f... more In this paper, apply an established transference principle to obtain the boundedness of certain functional calculi for the sequence of semigroup generators. It is proved that if be the sequence generates 0- semigroups on a Hilbert space, then for each the sequence of operators has bounded calculus for the closed ideal of bounded holomorphic functions on right half–plane. The bounded of this calculus grows at most logarithmically as. As a consequence decay at ∞. Then showed that each sequence of semigroup generator has a so-called (strong) m-bounded calculus for all m∈ℕ, and that this property characterizes the sequence of semigroup generators. Similar results are obtained if the underlying Banach space is a UMD space. Upon restriction to so-called semigroups, the Hilbert space results actually hold in general Banach spaces.
ScienceAsia, 2014
Bounded Composition operators usually induced by an analytic self-map of the open unit disk on th... more Bounded Composition operators usually induced by an analytic self-map of the open unit disk on the Hardy space 2 H and on the higher power weighted Bergman spaces 2 2 (1) 1 L . An inequality for the relationship between the norms of the corresponding operators on these spaces is considered.
Nonlinear Analysis: Theory, Methods & Applications, 2001
Chaos, Solitons & Fractals, 2002
Abstract This paper investigates the stability and Hopf bifurcation of a delay competition diffus... more Abstract This paper investigates the stability and Hopf bifurcation of a delay competition diffusion system. Firstly we discuss the existence and stability of the corresponding steady state solutions. Secondly our purpose is to give more detail information about the Hopf bifurcation of this system. We derive the basis of the eigenfunction subspace and then convert the existence of periodic solutions to the study of the existence of the implicit function. Finally, we analyze the stability of the periodic solutions by reducing the original system on the center manifold.
Oriental Journal of Physical Sciences, 2019
We show the validity of a complete description of closed ideals of the algebra is the algebra of ... more We show the validity of a complete description of closed ideals of the algebra is the algebra of series of analytic functions satisfying the Lipschitz condition of order αj2 obtained by.15
Abstract- In this paper we generalize the concepts of integrating of sequences of random variab... more Abstract- In this paper we generalize the concepts of integrating of sequences of random variables in nuclear spaces setting which satisfy with their strong duals the following conditions: the reflexivity, completeness and bornological spaces. Assume that there is a continuous bilinear mapping on the nuclear spaces. For an integrable, predictable processes and square integrable martingales, then there exists a process called the sequence of random variables integrals. The Lebesgue space of these integrable processes is studied and convergence theorems are given. Extensions to general locally convex spaces are presented.
Global Journal of Science Frontier Research, 2019
In this paper, apply an established transference principle to obtain the boundedness of certain f... more In this paper, apply an established transference principle to obtain the boundedness of certain functional calculi for the sequence of semigroup generators. It is proved thatif-í µí°´í µí°´íµí°´í µí±í µí± be the sequence generates í µí° ¶í µí° ¶ 0-semigroups on a Hilbert space, then for each í µí¼í µí¼ > −1 the sequence of operators í µí°´í µí°´íµí°´í µí±í µí± has bounded calculus for the closed ideal of bounded holomorphic functions on right half-plane. The bounded of this calculus grows at most logarithmically as(1 + í µí¼í µí¼) ↘ 0. As a consequence decay at ∞. Then showed that each sequence of semigroup generator has a so-called (strong) m-bounded calculus for all m ∈ ℕ, and that this property characterizes the sequence of semigroup generators. Similar results are obtained if the underlying Banach space is a UMD space. Upon restriction to so-called í µí»¾í µí»¾ í µí±í µí± − í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí± semigroups, the Hilbert space results actually hold in general Banach spaces. Abstract-In this paper, apply an established transference principle to obtain the boundedness of certain functional calculi for the sequence of semigroup generators. It is proved thatif-í µí±¨í µí±¨íµí±¨í µí²í µí² be the sequence generates í µí±ªí µí±ª í µí¿í µí¿-semigroups on a Hilbert space, then for each í µí¼ºí µí¼º > −1 the sequence of operators í µí±¨í µí±¨íµí±¨í µí²í µí² has bounded calculus for the closed ideal of bounded holomorphic functions on right half-plane. The bounded of this calculus grows at most logarithmically as(í µí¿í µí¿ + í µí¼ºí µí¼º) ↘ í µí¿í µí¿. As a consequence decay at ∞. Then showed that each sequence of semigroup generator has a so-called (strong) m-bounded calculus for all m ∈ ℕ, and that this property characterizes the sequence of semigroup generators. Similar results are obtained if the underlying Banach space is a UMD space. Upon restriction to so-calledí µí¼¸í µí¼¸íµí¼¸í µí²í µí² − í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí² semigroups, the Hilbert space results actually hold in general Banach spaces.
The description of the spectra tiling properties and Gabor orthonormal bases generated by the uni... more The description of the spectra tiling properties and Gabor orthonormal bases generated by the unit cubes and of the exponential for the 𝑛-cube are characterized. In addition the uniformity of non-uniform Gabor bases, atomic characterizations of modulation spaces through Gabor representations with Weyl-Heisenberg frames on Hilbert space, slanted matrices and Banach frames are clearly improved. We obtain the density, stability, generated characteristic function and Hamiltonian deformations of Gabor frames. We find estimates for vector –valued Gabor frames of Hermite functions plus periodic subsets of the real line. The Gabor frame sets for subspace with totally positive functions and deformation of Gabor systems are considered.
For describing the space (C[0,1],X) , where X is a Banach space, of absolutely summing operators ... more For describing the space (C[0,1],X) , where X is a Banach space, of absolutely summing operators from C[0, 1] to X in terms of the space X itself, we construct a tree space l1 (X) on X. It consists of special trees in X which we call two-trunk trees. We show that P(C[0,1],X)is isometrically isomorphic to l1 (X). As an application on [19], we characterize the bounded approximation property (BAP) and the weak BAP in terms of X-valued square sequence spaces.
Global Journal of Science Frontier Research, 2019
In this paper, apply an established transference principle to obtain the boundedness of certain f... more In this paper, apply an established transference principle to obtain the boundedness of certain functional calculi for the sequence of semigroup generators. It is proved that if be the sequence generates 0- semigroups on a Hilbert space, then for each the sequence of operators has bounded calculus for the closed ideal of bounded holomorphic functions on right half–plane. The bounded of this calculus grows at most logarithmically as. As a consequence decay at ∞. Then showed that each sequence of semigroup generator has a so-called (strong) m-bounded calculus for all m∈ℕ, and that this property characterizes the sequence of semigroup generators. Similar results are obtained if the underlying Banach space is a UMD space. Upon restriction to so-called semigroups, the Hilbert space results actually hold in general Banach spaces.
ScienceAsia, 2014
Bounded Composition operators usually induced by an analytic self-map of the open unit disk on th... more Bounded Composition operators usually induced by an analytic self-map of the open unit disk on the Hardy space 2 H and on the higher power weighted Bergman spaces 2 2 (1) 1 L . An inequality for the relationship between the norms of the corresponding operators on these spaces is considered.
Nonlinear Analysis: Theory, Methods & Applications, 2001
Chaos, Solitons & Fractals, 2002
Abstract This paper investigates the stability and Hopf bifurcation of a delay competition diffus... more Abstract This paper investigates the stability and Hopf bifurcation of a delay competition diffusion system. Firstly we discuss the existence and stability of the corresponding steady state solutions. Secondly our purpose is to give more detail information about the Hopf bifurcation of this system. We derive the basis of the eigenfunction subspace and then convert the existence of periodic solutions to the study of the existence of the implicit function. Finally, we analyze the stability of the periodic solutions by reducing the original system on the center manifold.
Oriental Journal of Physical Sciences, 2019
We show the validity of a complete description of closed ideals of the algebra is the algebra of ... more We show the validity of a complete description of closed ideals of the algebra is the algebra of series of analytic functions satisfying the Lipschitz condition of order αj2 obtained by.15
Abstract- In this paper we generalize the concepts of integrating of sequences of random variab... more Abstract- In this paper we generalize the concepts of integrating of sequences of random variables in nuclear spaces setting which satisfy with their strong duals the following conditions: the reflexivity, completeness and bornological spaces. Assume that there is a continuous bilinear mapping on the nuclear spaces. For an integrable, predictable processes and square integrable martingales, then there exists a process called the sequence of random variables integrals. The Lebesgue space of these integrable processes is studied and convergence theorems are given. Extensions to general locally convex spaces are presented.
Global Journal of Science Frontier Research, 2019
In this paper, apply an established transference principle to obtain the boundedness of certain f... more In this paper, apply an established transference principle to obtain the boundedness of certain functional calculi for the sequence of semigroup generators. It is proved thatif-í µí°´í µí°´íµí°´í µí±í µí± be the sequence generates í µí° ¶í µí° ¶ 0-semigroups on a Hilbert space, then for each í µí¼í µí¼ > −1 the sequence of operators í µí°´í µí°´íµí°´í µí±í µí± has bounded calculus for the closed ideal of bounded holomorphic functions on right half-plane. The bounded of this calculus grows at most logarithmically as(1 + í µí¼í µí¼) ↘ 0. As a consequence decay at ∞. Then showed that each sequence of semigroup generator has a so-called (strong) m-bounded calculus for all m ∈ ℕ, and that this property characterizes the sequence of semigroup generators. Similar results are obtained if the underlying Banach space is a UMD space. Upon restriction to so-called í µí»¾í µí»¾ í µí±í µí± − í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí± semigroups, the Hilbert space results actually hold in general Banach spaces. Abstract-In this paper, apply an established transference principle to obtain the boundedness of certain functional calculi for the sequence of semigroup generators. It is proved thatif-í µí±¨í µí±¨íµí±¨í µí²í µí² be the sequence generates í µí±ªí µí±ª í µí¿í µí¿-semigroups on a Hilbert space, then for each í µí¼ºí µí¼º > −1 the sequence of operators í µí±¨í µí±¨íµí±¨í µí²í µí² has bounded calculus for the closed ideal of bounded holomorphic functions on right half-plane. The bounded of this calculus grows at most logarithmically as(í µí¿í µí¿ + í µí¼ºí µí¼º) ↘ í µí¿í µí¿. As a consequence decay at ∞. Then showed that each sequence of semigroup generator has a so-called (strong) m-bounded calculus for all m ∈ ℕ, and that this property characterizes the sequence of semigroup generators. Similar results are obtained if the underlying Banach space is a UMD space. Upon restriction to so-calledí µí¼¸í µí¼¸íµí¼¸í µí²í µí² − í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí²í µí² semigroups, the Hilbert space results actually hold in general Banach spaces.