scholarly journals Fractal Frames of Functions on the Rectangle

2021 ◽  
Vol 5 (2) ◽  
pp. 42
Author(s):  
María A. Navascués ◽  
Ram Mohapatra ◽  
Md. Nasim Akhtar
Keyword(s):  
Tensor Product ◽  
Product Space ◽  
Integrable Function ◽  
Two Dimensional ◽  
Tensor Product Space ◽  
Fractal Functions

In this paper, we define fractal bases and fractal frames of L2(I×J), where I and J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification of L2(I×J) with the tensor product space L2(I)⨂L2(J). First, we recall the procedure of constructing a fractal perturbation of a continuous or integrable function. Then, we define fractal frames and bases of L2(I×J) composed of product of such fractal functions. We also obtain weaker families as Bessel, Riesz and Schauder sequences for the same space. Additionally, we study some properties of the tensor product of the fractal operators associated with the maps corresponding to each variable.

scholarly journals Applications of Multiparameter Eigenvalue Problems

2021 ◽  
Vol 19 (2) ◽  
pp. 75-82
Author(s):  
Niranjan Bora
Keyword(s):  
Tensor Product ◽  
Product Space ◽  
Eigenvalue Problems ◽  
Tensor Product Space ◽  
Mixed Eigenvalue

It was mainly due to Atkinson works, who introduced Linear Multiparameter Eigenvalue problems (LMEPs), based on determinantal operators on the Tensor Product Space. Later, in the area of Multiparameter eigenvalue problems has received attention from the Mathematicians in the recent years also, who pointed out that there exist a variety of mixed eigenvalue problems with several parameters in different scientific domains. This article aims to bring into a light variety of scientific problems that appear naturally as LMEPs. Of course, with all certainty, the list of collection of applications presented here are far from complete, and there are bound to be many more applications of which we are currently unaware. The paper may provide a review on applications of Multiparameter eigenvalue problems in different scientific domains and future possible applicatios both in theoretical and applied disciplines.

scholarly journals Parallelization in time through tensor-product space–time solvers

2008 ◽  
Vol 346 (1-2) ◽  
pp. 113-118 ◽  
Author(s):  
Yvon Maday ◽  
Einar M. Rønquist
Keyword(s):  
Tensor Product ◽  
Product Space ◽  
Space Time ◽  
Tensor Product Space

An abstract multiparameter spectral theory

1982 ◽  
Vol 92 (3-4) ◽  
pp. 193-204 ◽  
Author(s):  
P. A. Binding ◽  
A. Källström ◽  
B. D. Sleeman
Keyword(s):  
Eigenvalue Problem ◽  
Tensor Product ◽  
Spectral Theory ◽  
Hilbert Spaces ◽  
Product Space ◽  
Infinite Dimensions ◽  
Tensor Product Space ◽  
Image Position ◽  
Adjoint Operators

SynopsisWe consider the eigenvalue problemfor self-adjoint operators Ai and Bij on separable Hilbert spaces Hi. It is assumed that and Bij are bounded with compact. Various properties of the eigentuples λi, and xi are deduced under a “definiteness condition” weaker than those used by previous authors, at least in infinite dimensions. In particular, a Parseval relation and eigenvector expansion are derived in a suitably constructed tensor product space.

scholarly journals Lipschitz (q, p, E)-summing operators on injective Lipschitz tensor products of spaces

2020 ◽  
Vol 6 (1) ◽  
pp. 127-142
Author(s):  
Abdelhamid Tallab
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Product Space ◽  
Tensor Products ◽  
Injective Tensor Product ◽  
Mixing Operators ◽  
Tensor Product Space ◽  
Special Case

AbstractIn this paper, we introduce the notion of (q, p)-mixing operators from the injective tensor product space E ̂⊗∈F into a Banach space G which we call (q, p, F)-mixing. In particular, we extend the notion of (q, p, E)-summing operators which is a special case of (q, p, F)-mixing operators to Lipschitz case by studying their properties and showing some results for this notion.

TENSOR PRODUCT DECOMPOSITIONS FOR AFFINE KAC-MOODY ALGEBRAS

1994 ◽  
Vol 06 (06) ◽  
pp. 1269-1299 ◽  
Author(s):  
M. D. GOULD
Keyword(s):  
Tensor Product ◽  
Product Space ◽  
Virasoro Algebra ◽  
Moody Algebra ◽  
Product Decomposition ◽  
Highest Weight ◽  
Tensor Product Space ◽  
Irreducible Modules ◽  
Coset Construction ◽  
Highest Weight Modules

The decomposition into irreducible modules is determined, for the tensor product of two arbitrary irreducible integrable highest weight modules, for an (untwisted) affine Kac-Moody algebra L. The result is applied to investigate full multiplicity regions and cyclic modules within the tensor product space for an affine Kac-Moody algebra. The tensor product decomposition into irreducible modules over L ⊕ Vir (Coset construction), Vir the Virasoro algebra, is also briefly investigated.

The maximal C*-norm and the Haagerup norm

1990 ◽  
Vol 107 (1) ◽  
pp. 109-114 ◽  
Author(s):  
Takashi Itoh
Keyword(s):  
Tensor Product ◽  
Product Space ◽  
Finite Dimensional ◽  
Tensor Product Space ◽  
The Difference

AbstractThe difference between the maximal C*-norm ‖ ‖max and the Haagerup norm ‖ ‖h on the tensor product space of C*-aIgebras is studied. Let A and B be C*-algebras. It is shown that ‖ ‖max is equivalent to ‖ ‖h on A ⊗ B if and only if A or B is finite-dimensional.

scholarly journals Fusion frames and g-frames in tensor product and direct sum of Hilbert spaces

2012 ◽  
Vol 6 (2) ◽  
pp. 287-303
Author(s):  
Amir Khosravi ◽  
Azandaryani Mirzaee
Keyword(s):  
Tensor Product ◽  
Finite Number ◽  
Hilbert Spaces ◽  
Product Space ◽  
Tensor Products ◽  
Riesz Bases ◽  
Direct Sums ◽  
Fusion Frames ◽  
Direct Sum ◽  
Tensor Product Space

In this paper we study fusion frames and g-frames for the tensor products and direct sums of Hilbert spaces. We show that the tensor product of a finite number of g-frames (resp. fusion frames, g-Riesz bases) is a g-frame (resp. fusion frame, g-Riesz basis) for the tensor product space and vice versa. Moreover we obtain some important results in tensor products and direct sums of g-frames, fusion frames, resolutions of the identity and duals.

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