Finite absolute continuity of Gaussian measures on infinite-dimensional spaces

2008 ◽  
Vol 60 (10) ◽  
pp. 1592-1604
Author(s):  
G. V. Ryabov
Keyword(s):  
Absolute Continuity ◽  
Gaussian Measures ◽  
Infinite Dimensional

Absolute continuity of perturbed Gaussian measures

1998 ◽  
Vol 34 (2) ◽  
pp. 298-300
Author(s):  
V. G. Bondarenko
Keyword(s):  
Absolute Continuity ◽  
Gaussian Measures

p-ADIC HILBERT SPACE REPRESENTATION OF QUANTUM SYSTEMS WITH AN INFINITE NUMBER OF DEGREES OF FREEDOM

1996 ◽  
Vol 10 (13n14) ◽  
pp. 1665-1673 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
ANDREW KHRENNIKOV
Keyword(s):  
Hilbert Space ◽  
Infinite Number ◽  
Degrees Of Freedom ◽  
Quantum Systems ◽  
Space Representation ◽  
Gaussian Measures ◽  
Infinite Dimensional ◽  
Integrable Functions ◽  
Symmetric Operators ◽  
Square Integrable Functions

Gaussian measures on infinite-dimensional p-adic spaces are introduced and the corresponding L2-spaces of p-adic valued square integrable functions are constructed. Representations of the infinite-dimensional Weyl group are realized in p-adic L2-spaces. p-adic Hilbert space representations of quantum Hamiltonians for systems with an infinite number of degrees of freedom are constructed. Many Hamiltonians with potentials which are too singular to exist as functions over reals are realized as bounded symmetric operators in L2-spaces with respect to a p-adic Gaussian measure.

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