فهرست مطالب
مجله موجکها و جبر خطی
سال پنجم شماره 1 (Spring and Summer 2018)
- تاریخ انتشار: 1397/05/22
- تعداد عناوین: 6
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Pages 1-9We 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.Keywords: Singleton g_frame operator_Dual of a singleton g_frame_Singleton g_Riesz basis_Singleton g_orthonormal basis -
Pages 11-26Necessary conditions for shearlet and cone-adapted shearlet systems to be frames are presented with respect to the admissibility condition of generators.Keywords: Shearlet system, Cone, adapted shearlet system, Shearlet frame, Admissibility condition
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Pages 27-47In this article, we consider pair frames in Banach spaces and introduce Banach pair frames. Some various concepts in the frame theory such as frames, Schauder frames, Banach frames and atomic decompositions are considered as special kinds of (Banach) pair frames. Some frame-like inequalities for (Banach) pair frames are presented. The elements that participant in the construction of (Banach) pair frames are characterized. It is shown that a Banach space $\mathrm{X}$ has a Banach pair frame with respect to a Banach scalar sequence space $\ell$, when it is precisely isomorphic to a complemented subspace of $\ell$.
It is shown that if we are allowed to choose the scalar sequence space, pair frames and Banach pair frames with respect to the chosen scalar sequence space denote the same conceptKeywords: Banach frame, Atomic decomposition, (Banach)pair frame, (Banach)pair Bessel -
Pages 49-56In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and engineering problems.Keywords: Spectral function, Proximal average, Moreau envelope, Infimal convolution
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Pages 57-71The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are providedKeywords: Fourier transform, continuous p, adic shearlet transform, p, adic shearlet system
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Pages 73-87In this paper a new quantity for real tensors, the sign-real spectral radius, is defined and investigated. Various characterizations, bounds and some properties are derived. In certain aspects our quantity shows similar behavior to the spectral radius of a nonnegative tensor. In fact, we generalize the Perron Frobenius theorem for nonnegative tensors to the class of real tensors.Keywords: Higher order tensor, Nonnegative tensor, Perron Frobenius theorem