DUAL REPRESENTATION OF THE CURVATURE IN A HILBERT SPACE: CURVATURE AND INTEGRAL TRANSFORMS

2021 ◽  
Vol 26 (1) ◽  
pp. 39-51
Author(s):  
Francisco Bulnes
Keyword(s):  
Hilbert Space ◽  
Integral Transforms ◽  
Dual Representation ◽  
Space Curvature

scholarly journals Eigenfunction expansion of generalized functions

1978 ◽  
Vol 72 ◽  
pp. 1-25 ◽  
Author(s):  
J. N. Pandey ◽  
R. S. Pathak
Keyword(s):  
Hilbert Space ◽  
Eigenfunction Expansion ◽  
Orthogonal Series ◽  
Integral Transforms ◽  
Generalized Functions ◽  
Series Expansions ◽  
Schwartz Distributions ◽  
Space Technique

Expansions of generalized functions have been investigated by many authors. Korevaar [11], Widlund [20], Giertz [8], Walter [19] developed procedures for expanding generalized functions of Korevaar [12], Temple [17], and Lighthill [13], Expansions of certain Schwartz distributions [15] into series of orthonormal functions were given by Zemanian [23] (see also Zemanian [24]) and thereby he extended a number of integral transforms to distributions. The method involved in his work is very much related to the Hilbert space technique and is of somewhat different character from those used in most of the works on integral transforms such as [24, chapters 1-8]. Other works that discuss orthogonal series expansions involving generalized functions are by Bouix [1, chapter 7], Braga and Schönberg [2], Gelfand and Shilov [7, vol. 3, chapter 4] and Warmbrod [21].

scholarly journals A Note on Meromorphic Functions Associated With Beseel Function Defined by Hilbert Sapce Operator

2021 ◽  
Vol 8 (1) ◽  
pp. 66-76
Author(s):  
B. Venkateswarlu ◽  
P. Thirupathi Reddy ◽  
R. Madhuri Shilpa ◽  
G. Swapna
Keyword(s):  
Hilbert Space ◽  
Differential Operator ◽  
Meromorphic Functions ◽  
Integral Transforms ◽  
Distortion Theorem ◽  
Linear Combinations ◽  
Coefficient Inequality

Abstract In this paper,we introduce and study a new subclass of meromorphic functions associated with a certain differential operator on Hilbert space. For this class, we obtain several properties like the coefficient inequality, growth and distortion theorem, radius of close-to-convexity, starlikeness and meromorphically convexity and integral transforms. Further, it is shown that this class is closed under convex linear combinations.

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space
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