6 papers · 1 filter
Functional Models of Abelian Locally von Neumann Algebras and Direct Integrals of Locally Hilbert Spaces
Aurelian Gheondea, Chaitanya J. Kulkarni, Santhosh Kumar Pamula
We obtain a functional model for an arbitrary Abelian locally von Neumann algebra acting on a representing locally Hilbert space under the assumption that the index directed set is…
Localised Operator Valued Kernels Invariant under Actions of -Semigroupoids
Aurelian Gheondea
We consider positive semidefinite kernels which have values given by bounded linear operators on certain bundles of Hilbert spaces and which are invariant under actions of -semi…
An Operator Theoretical Approach to Mercer's Theorem
Aurelian Gheondea
This is a survey article on Mercer's Theorem in its most general form and its relations with the theory of reproducing kernel Hilbert spaces and the spectral theory of compact oper…
Representing Locally Hilbert Spaces and Functional Models for Locally Normal Operators
Aurelian Gheondea
The aim of this article is to explore in all remaining aspects the spectral theory of locally normal operators. In a previous article we proved the spectral theorem in terms of loc…
Localisation of Regularised and Multiview Support Vector Machine Learning
Aurelian Gheondea, Cankat Tilki
We prove a few representer theorems for a localised version of the regularised and multiview support vector machine learning problem introduced by H.Q. Minh, L. Bazzani, and V. Mur…
Notes on (the Birmak-Krein-Vishik theory on) selfadjoint extensions of semibounded symmetric operators
Tiberiu Constantinescu, Aurelian Gheondea
We give an explicit and versatile parametrization of all positive selfadjoint extensions of a densely defined, closed, positive operator. In addition, we identify the Friedrichs ex…