Dual basis functions in subspaces of inner product spaces

2013 ◽  
Vol 219 (19) ◽  
pp. 10012-10024 ◽  
Author(s):  
Scott N. Kersey
Keyword(s):  
Basis Functions ◽  
Inner Product ◽  
Product Spaces ◽  
Dual Basis ◽  
Inner Product Spaces

Indexed Families of Functionals and Gaussian Radial Basis Functions

2003 ◽  
Vol 15 (2) ◽  
pp. 455-468 ◽  
Author(s):  
Irwin W. Sandberg
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Basis Functions ◽  
Inner Product ◽  
Radial Basis Function Networks ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Finite Dimensional ◽  
Radial Basis

We report on results concerning the capabilities of gaussian radial basis function networks in the setting of inner product spaces that need not be finite dimensional. Specifically, we show that important indexed families of functionals can be uniformly approximated, with the approximation uniform also with respect to the index. Applications are described concerning the classification of signals and the synthesis of reconfigurable classifiers.

scholarly journals Fuzzy Inner Product Space: Literature Review and a New Approach

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 765
Author(s):  
Lorena Popa ◽  
Lavinia Sida
Keyword(s):  
Literature Review ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Comprehensive Overview ◽  
New Approach ◽  
Inner Product Spaces ◽  
Product Function ◽  
Suitable Definition

The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta’s definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type Nădăban-Dzitac. Finally, some challenges are given.

Triangle Congruence Characterizations of Inner Product Spaces

1989 ◽  
Vol 144 (1) ◽  
pp. 81-86
Author(s):  
Charles R. Diminnie ◽  
Edward Z. Andalafte ◽  
Raymond W. Freese
Keyword(s):  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces
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