scholarly journals On self-adjoint operators in Krein spaces constructed by Clifford algebra Cl_2

2012 ◽  
Vol 32 (2) ◽  
pp. 297 ◽  
Author(s):  
Sergii Kuzhel ◽  
Olexiy Patsyuck
Keyword(s):  
Clifford Algebra ◽  
Krein Spaces ◽  
Adjoint Operators

scholarly journals Spectral points of type π+ and π- of self-adjoint operators in Krein spaces

2005 ◽  
Vol 226 (1) ◽  
pp. 114-137 ◽  
Author(s):  
Tomas Ya. Azizov ◽  
Peter Jonas ◽  
Carsten Trunk
Keyword(s):  
Krein Spaces ◽  
Adjoint Operators

On J-self-adjoint operators with stable C-symmetries

2013 ◽  
Vol 143 (1) ◽  
pp. 141-167 ◽  
Author(s):  
Seppo Hassi ◽  
Sergii Kuzhel
Keyword(s):  
Symmetric Operator ◽  
Reproducing Kernel ◽  
Boundary Value ◽  
Functional Model ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Krein Spaces ◽  
Adjoint Operators

The paper is devoted to the development of the theory of self-adjoint operators in Krein spaces (J-self-adjoint operators) involving some additional properties arising from the existence of C-symmetries. We mainly focus on the recent notion of stable C-symmetry for J-self-adjoint extensions of a symmetric operator S. The general results involve boundary value techniques and reproducing kernel space methods, and they include an explicit functional model for the class of stable C-symmetries. Some of the results are specialized further by studying the case where S has defect numbers 〈2,2〉 in detail.

Spectrum of definite type of self-adjoint operators in Krein spaces

2005 ◽  
Vol 53 (2) ◽  
pp. 115-136 ◽  
Author(s):  
Heinz Langer ◽  
Matthias Langer ◽  
Alexander Markus ◽  
Christiane Tretter
Keyword(s):  
Krein Spaces ◽  
Adjoint Operators

Some shaper uncertainty principles for multivector-valued functions

2016 ◽  
Vol 14 (06) ◽  
pp. 1650043
Author(s):  
Minggang Fei ◽  
Yubin Pan ◽  
Yuan Xu
Keyword(s):  
Fourier Transform ◽  
Clifford Algebra ◽  
Uncertainty Principle ◽  
Dunkl Transform ◽  
Uncertainty Principles ◽  
Heisenberg Uncertainty Principle ◽  
Clifford Fourier Transform ◽  
Heisenberg Uncertainty ◽  
The Fourier Transform ◽  
Adjoint Operators

The Heisenberg uncertainty principle and the uncertainty principle for self-adjoint operators have been known and applied for decades. In this paper, in the framework of Clifford algebra, we establish a stronger Heisenberg–Pauli–Wely type uncertainty principle for the Fourier transform of multivector-valued functions, which generalizes the recent results about uncertainty principles of Clifford–Fourier transform. At the end, we consider another stronger uncertainty principle for the Dunkl transform of multivector-valued functions.

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

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