Ornstein-Uhlenbeck Semigroup on the dual space of Gelfand-Shilov Spaces of Beurling type

2021 ◽  
Vol 39 (1) ◽  
pp. 71-80
Author(s):  
Hamed M. Obiedat ◽  
Lloyd E. Moyo
Keyword(s):  
Representation Theorem ◽  
Weak Topology ◽  
Dual Space ◽  
Riesz Representation Theorem ◽  
Topological Characterization ◽  
Riesz Representation

We use a previously obtained topological characterization of Gelfand-Shilov spaces of Beurling type to characterize its dual  using Riesz representation theorem. Using the characterization of the dual space equipped with the weak topology, we study the action of Ornstein-Uhlenbeck Semigroup on the dual space.

scholarly journals Structure Theorem for Functionals in the Space

2008 ◽  
Vol 2008 ◽  
pp. 1-9
Author(s):  
Hamed M. Obiedat ◽  
Wasfi A. Shatanawi ◽  
Mohd M. Yasein
Keyword(s):  
Dual Space ◽  
Structure Theorem ◽  
Topological Characterization ◽  
Riesz Representation

We introduce the space of all functions such that and are finite for all , , where and are two weights satisfying the classical Beurling conditions. Moreover, we give a topological characterization of the space without conditions on the derivatives. For functionals in the dual space , we prove a structure theorem by using the classical Riesz representation thoerem.

Characterization of the w-Tempered ultradistributions

2021 ◽  
Vol 39 (2) ◽  
pp. 133-140
Author(s):  
Ibraheem Amohammad Abu-Falahah ◽  
Hamed M. Obiedat
Keyword(s):  
Representation Theorem ◽  
Riesz Representation Theorem ◽  
Test Functions ◽  
Riesz Representation ◽  
Tempered Ultradistributions

We use apreviously obtained characterization of test functions of w-Tempered Ultradistributions to charcterize the space w-Tempered Ultradistributions using Riesz representation Theorem.

Hilbert Spaces

2021 ◽  
pp. 290-340
Author(s):  
Adel N. Boules
Keyword(s):  
Hilbert Spaces ◽  
Representation Theorem ◽  
Compact Operators ◽  
Projection Operators ◽  
Riesz Representation Theorem ◽  
Introductory Course ◽  
Normal Operators ◽  
Riesz Representation ◽  
Alternative Approaches

This chapter is a good introduction to Hilbert spaces and the elements of operator theory. The two leading sections contains staple topics such as the projection theorem, projection operators, the Riesz representation theorem, Bessel’s inequality, and the characterization of separable Hilbert spaces. Sections 7.3 and 7.4 contain a rather detailed study of self-adjoint and compact operators. Among the highlights are the Fredholm theory and the spectral theorems for compact self-adjoint and normal operators, with applications to integral equations. The section exercises contain problems that suggest alternative approaches, thus allowing the instructor to shorten the chapter while preserving good depth. The last section extends the results to compact operators on Banach spaces. The chapter contains more results than is typically found in an introductory course.

ON THE RIESZ REPRESENTATION THEOREM IN TOPOLOGICAL VECTOR SPACES

2000 ◽  
Vol 36 (3-4) ◽  
pp. 347-352
Author(s):  
M. A. Alghamdi ◽  
L. A. Khan ◽  
H. A. S. Abujabal
Keyword(s):  
Representation Theorem ◽  
Type Theorem ◽  
Representation Type ◽  
Vector Spaces ◽  
Riesz Representation Theorem ◽  
Topological Vector Spaces ◽  
Riesz Representation

I this paper we establish a Riesz representation type theorem which characterizes the dual of the space C rc (X,E)endowed with the countable-ope topologyi the case of E ot ecessarilya locallyconvex TVS.

Yet another short proof of the Riesz representation theorem

1989 ◽  
Vol 105 (1) ◽  
pp. 139-140 ◽  
Author(s):  
David Ross
Keyword(s):  
Representation Theorem ◽  
Short Proof ◽  
Riesz Representation Theorem ◽  
Riesz Theorem ◽  
Riesz Representation

F. Riesz's ‘Representation Theorem’ has been proved by methods classical [11, 12], category-theoretic [7], and functional-analytic [2, 9]. (Garling's remarkable proofs [5, 6] owe their brevity to the combined strength of these and other methods.) These proofs often reveal a connection between the Riesz theorem and some unexpected area of mathematics.

A nonstandard proof of the Riesz representation theorem for weakly compact operators on C(Ω)

1989 ◽  
Vol 105 (1) ◽  
pp. 141-145
Author(s):  
Yeneng Sun
Keyword(s):  
Representation Theorem ◽  
Compact Operators ◽  
Riesz Representation Theorem ◽  
Linear Functionals ◽  
Weakly Compact ◽  
Vector Measures ◽  
Riesz Representation ◽  
Weakly Compact Operators ◽  
Measure Technique

AbstractAn easy way to construct the representing vector measures of weakly compact operators on C(Ω) is given by using the Loeb measure technique. This construction is not based on the Riesz representation theorem for linear functionals; thus we have a uniform way to treat the scalar and vector cases. Also the star finite representations of regular vector measures follow from the proof.

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