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We introduce the concept of the touching of two multifunctions on a real Hilbert space, and deduce that certain multifunctions on the space have a unique fixed point. These result are applied to the theory of genaralized cycles and…
A generalization with singular weights of Moore-Penrose generalized inverses of closed range operators in Hilbert spaces is studied using the notion of compatibility of subspaces and positive operators.
The study of infinitesimal deformations of a variety embedded in projective space requires that of deformations of a collection of points, as specified by a zero-dimensional scheme. Further, basic problems in infinitesimal interpolation…
We prove that the set of orthogonal projections on a Hilbert space equipped with the length metric is $\frac\pi2$-geodesic. As an application, we consider the problem of variation of spectral subspaces for bounded linear self-adjoint…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
The aim of this paper is to present an explicit reduction algorithm for Hilbert modular groups over arbitrary totally real number fields. An implementation of the algorithm is available to download from [19]. The exposition is…
In this paper, we characterize Probabilistic Principal Component Analysis in Hilbert spaces and demonstrate how the optimal solution admits a representation in dual space. This allows us to develop a generative framework for kernel methods.…
We discuss some perturbation results concerning certain pairs of sequences of vectors in a Hilbert space $\Hil$ and producing new sequences which share, with the original ones, { reconstruction formulas on a dense subspace of $\Hil$ or on…
In this paper we introduce and study a new kind of generalized Hilbert matrix operators, induced by a positive finite Borel measure on (0,1), acting on weighted sequence spaces. We establish a sufficient and necessary condition for the…
If $I=(f_1,\ldots,f_r)$ is an ideal in $S=k[x_1,\ldots,x_n]$, and $f_i$ are "general" elements of given degrees, there is a conjecture on the Hilbert series of $S/I$. We are considering the corresponding concepts in bigraded rings.
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…
We introduce weighted cb maps and $\Lambda_\mu$-cb maps on operator spaces which are generalizations of completely bounded maps and a certain class of bilinear maps on operator spaces which we call $\lambda_\mu$-cb bilinear maps. Some basic…
In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly and linearly regular sequences of operators. We show that the type of…
We study Hilbert functions of certain non-reduced schemes A supported at finite sets of points in projective space, in particular, fat point schemes. We give combinatorially defined upper and lower bounds for the Hilbert function of A using…
The aim of this paper is to study $K$-frames for quaternionic Hilbert spaces. First, we present the quaternionic version of Douglas's theorem and then investigate $K$-frames for a quaternionic Hilbert space $\mathcal{H}$, where $K \in…
In this paper we study $A$-projections, i.e. operators of a Hilbert space $\HH$ which act as projections when a seminorm is considered in $\HH$. $A$-projections were introduced by Mitra and Rao \cite{[MitRao74]} for finite dimensional…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…
We discuss the possibility of introducing a multi-resolution in a Hilbert space which is not necessarily a space of functions. We investigate which of the classical properties can be translated to this more general framework and the way in…
This paper presents an approach for inferring geometric constraints in human demonstrations. In our method, geometric constraint models are built to create representations of kinematic constraints such as fixed point, axial rotation,…