scholarly journals Scattering theory for a class of non-selfadjoint extensions of symmetric operators

2020 ◽  
pp. 194-230
Author(s):  
Kirill D. Cherednichenko ◽  
Alexander V. Kiselev ◽  
Luis O. Silva
Keyword(s):  
Scattering Theory ◽  
Symmetric Operators ◽  
Selfadjoint Extensions

scholarly journals Functional model for extensions of symmetric operators and applications to scattering theory

2018 ◽  
Vol 13 (2) ◽  
pp. 191-215 ◽  
Author(s):  
Kirill D. Cherednichenko ◽  
◽  
Alexander V. Kiselev ◽  
Luis O. Silva ◽  
◽  
...  
Keyword(s):  
Scattering Theory ◽  
Functional Model ◽  
Symmetric Operators

scholarly journals Correct selfadjoint and positive extensions of nondensely defined minimal symmetric operators

2005 ◽  
Vol 2005 (7) ◽  
pp. 767-790 ◽  
Author(s):  
I. Parassidis ◽  
P. Tsekrekos
Keyword(s):  
Hilbert Space ◽  
Symmetric Operator ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Selfadjoint Extension ◽  
Symmetric Operators ◽  
Selfadjoint Extensions ◽  
Positive Extensions

LetA0be a closed, minimal symmetric operator from a Hilbert spaceℍintoℍwith domain not dense inℍ. LetA^also be a correct selfadjoint extension ofA0. The purpose of this paper is (1) to characterize, with the help ofA^, all the correct selfadjoint extensionsBofA0with domain equal toD(A^), (2) to give the solution of their corresponding problems, (3) to find sufficient conditions forBto be positive (definite) whenA^is positive (definite).

scholarly journals Positive selfadjoint extensions of positive symmetric operators

1970 ◽  
Vol 22 (1) ◽  
pp. 65-75 ◽  
Author(s):  
Tsuyoshi Ando ◽  
Katsuyoshi Nishio
Keyword(s):  
Symmetric Operators ◽  
Selfadjoint Extensions

Smooth derivations commuting with Lie group actions

1986 ◽  
Vol 99 (2) ◽  
pp. 307-314
Author(s):  
F. M. Goodman ◽  
P. E. T. Jorgensen ◽  
C. Peligrad
Keyword(s):  
Hilbert Space ◽  
Unitary Representation ◽  
Lie Group ◽  
Scattering Theory ◽  
Relativistic Quantum ◽  
Quantum Scattering ◽  
Quantum Scattering Theory ◽  
Lie Group Actions ◽  
Physical Setting ◽  
Symmetric Operators

N. S. Poulsen, motivated in part by questions from relativistic quantum scattering theory, studied symmetric operators S in Hilbert space commuting with a unitary representation U of a Lie group G. (The group of interest in the physical setting is the Poincaré group.) He proved ([17], corollary 2·2) that if S is defined on the space of C∞-vectors for U (i.e. D(S) ⊇ ℋ∞(U)), then S is essentially self-adjoint.

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