scholarly journals Parseval's equality in fuzzy normed linear spaces

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 47-57
Author(s):  
Daraby Bayaz ◽  
Delzendeh Fataneh ◽  
Rahimi Asghar
Keyword(s):  
Hilbert Space ◽  
Vector Space ◽  
Hilbert Spaces ◽  
Continuous Functions ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Parseval’S Equality

We investigate Parseval's equality and define the fuzzy frame on Felbin fuzzy Hilbert spaces. We prove that C(Omega) (the vector space of all continuous functions on Omega) is normable in a Felbin fuzzy Hilbert space and so defining fuzzy frame on C(Omega) is possible. The consequences for the category of fuzzy frames in Felbin fuzzy Hilbert spaces are wider than for the category of the frames in the classical Hilbert spaces.

scholarly journals More on Continuous Functions on Normed Linear Spaces

2011 ◽  
Vol 19 (1) ◽  
Author(s):  
Hiroyuki Okazaki ◽  
Noboru Endou ◽  
Yasunari Shidama
Keyword(s):  
Continuous Functions ◽  
Linear Spaces ◽  
Normed Linear Spaces

scholarly journals Mean value properties of generalised eigenfunctions

1970 ◽  
Vol 17 (2) ◽  
pp. 155-158 ◽  
Author(s):  
Eberhard Gerlach
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Selfadjoint Operator ◽  
Differential Operators ◽  
Continuous Functions ◽  
Mean Value ◽  
Mean Value Property ◽  
Spaces Of Continuous Functions

Some Hilbert spaces of continuous functions satisfying a mean value property are studied in which the generalised eigenfunctions of any selfadjoint operator again satisfy the same mean value property. Applications are made to nullspaces of some differential operators. The classes of functions involved in these applications are less general than those studied by K. Maurin (6); however, the Hilbert space norms may be arbitrary, while Maurin only considered L2-norms.

On Best Simultaneous Approximation in Normed Linear Spaces

1974 ◽  
Vol 17 (4) ◽  
pp. 523-527 ◽  
Author(s):  
D. S. Goel ◽  
A. S. B. Holland ◽  
C. Nasim ◽  
B. N. Sahney
Keyword(s):  
Simultaneous Approximation ◽  
Continuous Functions ◽  
Supremum Norm ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Best Simultaneous Approximation ◽  
Image Position

Let S be a non-empty family of real valued continuous functions on [a, b]. Diaz and McLaughlin [1], [2], and Dunham [3] have considered the problem of simultaneously approximating two continuous functions f1 and f2 by elements of S. If || • || denotes the supremum norm, then the problem is to find an element * ∈ S if it exists, for which

scholarly journals The 2-Hilbert space of a prequantum bundle gerbe

2018 ◽  
Vol 30 (01) ◽  
pp. 1850001 ◽  
Author(s):  
Severin Bunk ◽  
Christian Sämann ◽  
Richard J. Szabo
Keyword(s):  
Hilbert Space ◽  
Line Bundle ◽  
Vector Space ◽  
Hilbert Spaces ◽  
Dimensional Reduction ◽  
Monoidal Structure ◽  
Bundle Gerbe ◽  
Closed Structure ◽  
Dual Functor ◽  
Bundle Gerbes

We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier–Douady class is torsion. Analogously to usual prequantization, this 2-Hilbert space has the category of sections of the line bundle gerbe as its underlying 2-vector space. These sections are obtained as certain morphism categories in Waldorf’s version of the 2-category of line bundle gerbes. We show that these morphism categories carry a monoidal structure under which they are semisimple and abelian. We introduce a dual functor on the sections, which yields a closed structure on the morphisms between bundle gerbes and turns the category of sections into a 2-Hilbert space. We discuss how these 2-Hilbert spaces fit various expectations from higher prequantization. We then extend the transgression functor to the full 2-category of bundle gerbes and demonstrate its compatibility with the additional structures introduced. We discuss various aspects of Kostant–Souriau prequantization in this setting, including its dimensional reduction to ordinary prequantization.

scholarly journals BEST COAPPROXIMATION IN METRIC LINEAR SPACES

1999 ◽  
Vol 30 (4) ◽  
pp. 241-252
Author(s):  
T. D. NARANG ◽  
S. P. SINGH
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Best Coapproximation

In order to obtain some characterizations of real Hilbert spaces among real Banach spaces, a new kind of approximation, called best coapproximation, was introduced in normed linear spaces by C. Franchetti and M. Furi [3] in 1972. Subsequently, the study was pursued in normed linear spaces and Hilbert spaces by H. Berens, L. Hetzelt, T. D. Narang, P. L. Papini, Gectha S. Rao and her students, Ivan Singer and a few others (see, e.g., [1], [4], [7], [9], [13 to 15], and [17 to 20]). In this paper, we discuss best coapproximation in metric linear spaces thereby generalizing some of the results proved in [3], [7], [13], and [18]. The problems considered are those of existence of elements of best coapproximation and their characterization, characteriza­ tions of coproximinal, co-semi-Chebyshev and co-Chebyshev subspaces, and some properties of the best coapproximation map in metric linears space.

Atomic Decompositions of Fuzzy Normed Linear Spaces for Wavelet Applications

Informatica ◽  
2014 ◽  
Vol 25 (4) ◽  
pp. 643-662 ◽  
Author(s):  
Sorin Nădăban ◽  
Ioan Dzitac
Keyword(s):  
Atomic Decompositions ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Wavelet Applications

scholarly journals Translation and modulation invariant Hilbert spaces

2021 ◽  
Author(s):  
Joachim Toft ◽  
Anupam Gumber ◽  
Ramesh Manna ◽  
P. K. Ratnakumar
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Zero Element ◽  
Multiplicative Constant ◽  
Space Of Distributions ◽  
Feichtinger Algebra

AbstractLet $$\mathcal H$$ H be a Hilbert space of distributions on $$\mathbf{R}^{d}$$ R d which contains at least one non-zero element of the Feichtinger algebra $$S_0$$ S 0 and is continuously embedded in $$\mathscr {D}'$$ D ′ . If $$\mathcal H$$ H is translation and modulation invariant, also in the sense of its norm, then we prove that $$\mathcal H= L^2$$ H = L 2 , with the same norm apart from a multiplicative constant.

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