28 citations · 76 across the 21 of their papers we have counts for
22 papers
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…
Forcing confidence: a Process Tracing approach with a dynamical systems model
Alexandra Gheondea-Eladi, Aurelian Gheondea
We propose a continuous time dynamical system model for tracing the evolution of confidence in a small decision making group by consensus with the possibility that a forcing factor…
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…
Partially Positive Semidefinite Maps on -Semigroupoids and Linearisations
Aurelian Gheondea, Bogdan Udrea
Motivated by Cuntz-Krieger-Toeplitz systems associated to undirected graphs and representations of groupoids, we obtain a generalisation of the Sz-Nagy's Dilation Theorem for opera…
Probability error bounds for approximation of functions in reproducing kernel Hilbert spaces
Ata Deniz Aydin, Aurelian Gheondea
We find probability error bounds for approximations of functions in a separable reproducing kernel Hilbert space with reproducing kernel on a base space ,…
A Comparison of Two Generalisations of Triplets of Hilbert Spaces
Petru Cojuhari, Aurelian Gheondea
We compare the concept of triplet of closely embedded Hilbert spaces with that of generalised triplet of Hilbert spaces in the sense of Berezanskii by showing when they coincide, w…
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…
Invariant Weakly Positive Semidefinite Kernels with Values in Topologically Ordered -Spaces
Serdar Ay, Aurelian Gheondea
We consider weakly positive semidefinite kernels valued in ordered -spaces with or without certain topological properties, and investigate their linearisations (Kolmogorov decom…
On Propagation of Fixed Points of Quantum Operations and Beyond
Aurelian Gheondea
We show that some abstract results on propagation of fixed points for completely positive maps on -algebras provide a natural approach to unify recent Noether type theorems on…
Operator Models for Hilbert Locally -Modules
Aurelian Gheondea
We single out the concept of concrete Hilbert module over a locally -algebra by means of locally bounded operators on certain strictly inductive limits of Hilbert spaces. Usin…
On the Dynamics of a Third Order Newton's Approximation Method
Aurelian Gheondea, Mehmet Emre Şamcı
We show that the third order approximation function , proposed by S. Amat, S. Busquier, S. Plaza, in \textit{J. Math. Anal. Appl.}, 366(2010), 24--32, for functions twice…
Representations of *-semigroups associated to invariant kernels with values continuously adjointable operators
Serdar Ay, Aurelian Gheondea
We consider positive semidefinite kernels valued in the -algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes)…
Representations of -semigroups associated to invariant kernels with values adjointable operators. I
Serdar Ay, Aurelian Gheondea
We consider positive semidefinite kernels valued in the -algebra of adjointable operators on a VE-space (Vector Euclidean space) and that are invariant under actions of -semi…
Interpolation for completely positive maps: numerical solutions
Calin-Grigore Ambrozie, Aurelian Gheondea
We present certain techniques to find completely positive maps between matrix algebras that take prescribed values on given data. To this aim we describe a semidefinite programming…
A Survey on Reproducing Kernel Krein Spaces
Aurelian Gheondea
This is a survey on reproducing kernel Krein spaces and their interplay with operator valued Hermitian kernels. Existence and uniqueness properties are carefully reviewed. The appr…
Triplets of Closely Embedded Hilbert Spaces
Petru Cojuhari, Aurelian Gheondea
We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoin…
An Interpolation Problem for Completely Positive Maps on Matrix Algebras: Solvability and Parametrisation
Calin-Grigore Ambrozie, Aurelian Gheondea
We present certain existence criteria and parameterisations for an interpolation problem for completely positive maps that take given matrices from a finite set into prescribed mat…
On L. Schwartz's boundedness condition for kernels
T. Constantinescu, A. Gheondea
In previous works we analysed conditions for linearization of hermitian kernels. The conditions on the kernel turned out to be of a type considered previously by L. Schwartz in the…
Representations of hermitian kernels by means of Krein spaces II. Invariant kernels
Tiberiu Constantinescu, Aurelian Gheondea
In this paper we study hermitian kernels invariant under the action of a semigroup with involution. We characterize those hermitian kernels which realize the given action by bounde…