Related papers: Analysis of parametric models for coupled systems

In this paper a new general approach is developed to construct and study Lebesgue type decompositions of linear operators $T$ in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue type…

In this paper, we study composition operators on Hilbert space of complex-valued harmonic functions. In particular, we explore isometries, the type of self-map that generate bounded composition operator, and characterize the boundedness of…

We discuss a (i) quantized version of the Jordan decomposition theorem for a complex Borel measure on a compact Hausdorff space, namely, the more general problem of decomposing a general noncommutative kernel (a quantization of the standard…

Frame theory provides a robust method for recovering vectors in a Hilbert space from inner product data, though the associated decomposition formula can be computationally demanding. We relax the frame condition by studying sequences that…

Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…

Joint spectra of tuples of operators are subsets in complex projective space. The corresponding tuple of operators can be viewed as an infinite dimensional analog of a determinantal representation of the joint spectrum. We investigate the…

This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear…

We present a general class of machine learning algorithms called parametric matrix models. In contrast with most existing machine learning models that imitate the biology of neurons, parametric matrix models use matrix equations that…

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…

We study sequences of bounded operators \((T_n)_{n \ge 0}\) on a complex separable Hilbert space \(\mathcal{H}\) that satisfy a linear recurrence relation of the form $$ T_{n+r} = A_0 T_n + A_1 T_{n+1} + \cdots + A_{r-1} T_{n+r-1}…

We consider the response of a multicomponent body to $n$ fields, such as electric fields, magnetic fields, temperature gradients, concentration gradients, etc., where each component, which is possibly anisotropic, may cross couple the…

A majority of shape correspondence frameworks are based on devising pointwise and pairwise constraints on the correspondence map. The functional maps framework allows for formulating these constraints in the spectral domain. In this paper,…

We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and…

A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…

This study deals with the missing link prediction problem: the problem of predicting the existence of missing connections between entities of interest. We address link prediction using coupled analysis of relational datasets represented as…

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…

In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…

We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…

Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogonal group representations on the other hand. In this way,…

Let $G$ be a locally compact abelian group with a Haar measure, and $Y$ be a measure space. Suppose that $H$ is a reproducing kernel Hilbert space of functions on $G\times Y$, such that $H$ is naturally embedded into $L^2(G\times Y)$ and is…