scholarly journals Representations of ⁎-semigroups associated to invariant kernels with values adjointable operators

2015 ◽  
Vol 486 ◽  
pp. 361-388 ◽  
Author(s):  
Serdar Ay ◽  
Aurelian Gheondea
Keyword(s):  
Invariant Kernels

scholarly journals Isomorphisms between determinantal point processes with translation-invariant kernels and Poisson point processes

2020 ◽  
pp. 1-14
Author(s):  
SHOTA OSADA
Keyword(s):  
Point Processes ◽  
Duke Math ◽  
Random Point ◽  
Determinantal Point Processes ◽  
Fredholm Determinants ◽  
Poisson Point Processes ◽  
Translation Invariant ◽  
Ergodic Properties ◽  
Tree Representations ◽  
Invariant Kernels

Abstract We prove the Bernoulli property for determinantal point processes on $ \mathbb{R}^d $ with translation-invariant kernels. For the determinantal point processes on $ \mathbb{Z}^d $ with translation-invariant kernels, the Bernoulli property was proved by Lyons and Steif [Stationary determinantal processes: phase multiplicity, bernoullicity, and domination. Duke Math. J.120 (2003), 515–575] and Shirai and Takahashi [Random point fields associated with certain Fredholm determinants II: fermion shifts and their ergodic properties. Ann. Probab.31 (2003), 1533–1564]. We prove its continuum version. For this purpose, we also prove the Bernoulli property for the tree representations of the determinantal point processes.

On reducing submodules of Hilbert modules withSn-invariant kernels

2019 ◽  
Vol 276 (3) ◽  
pp. 751-784
Author(s):  
Shibananda Biswas ◽  
Gargi Ghosh ◽  
Gadadhar Misra ◽  
Subrata Shyam Roy
Keyword(s):  
Hilbert Modules ◽  
Invariant Kernels

scholarly journals Tensor algebras and displacement structure. IV. Invariant kernels

2005 ◽  
Vol 405 ◽  
pp. 83-103
Author(s):  
T. Banks ◽  
T. Constantinescu ◽  
Nermine El-Sissi
Keyword(s):  
Displacement Structure ◽  
Tensor Algebras ◽  
Invariant Kernels

scholarly journals VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES AND UNIVERSALITY

2010 ◽  
Vol 08 (01) ◽  
pp. 19-61 ◽  
Author(s):  
C. CARMELI ◽  
E. DE VITO ◽  
A. TOIGO ◽  
V. UMANITÀ
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Abelian Groups ◽  
Reproducing Kernel Hilbert Spaces ◽  
Feature Maps ◽  
Translation Invariant ◽  
Kernel Hilbert Spaces ◽  
Vector Valued ◽  
Invariant Kernels

This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular, we characterize the structure of translation invariant kernels on abelian groups and we relate it to the universality problem.

Semidirect product invariant kernels

1975 ◽  
Vol 26 (6) ◽  
pp. 602-606
Author(s):  
L. M. Korsunskii
Keyword(s):  
Semidirect Product ◽  
Invariant Kernels
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