Implicit Resolvent Equation Problem in Hilbert Spaces Implicit Resolvent Equation Problem in Hilbert Spaces

2017 ◽  
Vol 6 (2) ◽  
pp. 141-147
Author(s):  
Iqbal Ahmad ◽  
Rais Ahmad ◽  
Mijanur Rahaman
Keyword(s):  
Hilbert Spaces ◽  
Resolvent Equation ◽  
Equation Problem

scholarly journals Sensitivity Analysis of Mixed Cayley Inclusion Problem with XOR-Operation

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 220
Author(s):  
Imran Ali ◽  
Mohd. Ishtyak ◽  
Rais Ahmad ◽  
Ching-Feng Wen
Keyword(s):  
Applied Sciences ◽  
Sensitivity Analysis ◽  
Climate Models ◽  
Inclusion Problem ◽  
Resolvent Equation ◽  
Operator Inclusion ◽  
Equation Problem ◽  
Xor Operation ◽  
Alternative Approach ◽  
Exclusive Or

In this paper, we consider the parametric mixed Cayley inclusion problem with Exclusive or (XOR)-operation and show its equivalence with the parametric resolvent equation problem with XOR-operation. Since the sensitivity analysis, Cayley operator, inclusion problems, and XOR-operation are all applicable for solving many problems occurring in basic and applied sciences, such as financial modeling, climate models in geography, analyzing “Black Box processes”, computer programming, economics, and engineering, etc., we study the sensitivity analysis of the parametric mixed Cayley inclusion problem with XOR-operation. For this purpose, we use the equivalence of the parametric mixed Cayley inclusion problem with XOR-operation and the parametric resolvent equation problem with XOR-operation, which is an alternative approach to study the sensitivity analysis. In support of some of the concepts used in this paper, an example is provided.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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