Related papers: Norm kernels and the closeness relation for Pauli-…
A hypothetical exclusion principle for quantum particles is introduced that generalizes the exclusion and inclusion principles for fermions and bosons, respectively: the correlated exclusion principle. The sum-free condition for Schur…
In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…
We extend the adjoint method to complex-valued PDEs and introduce the Fr\'echet root sensitivity kernel, as the most fundamental kernel from which all other material-sensitivity kernels can be derived. We apply this framework to four…
We present an operator-free, measure-theoretic approach to the conditional mean embedding (CME) as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of unconditional distributions has…
Contragenic functions are defined to be reduced-quaternion-valued harmonic functions which are orthogonal to all monogenic and antimonogenic functions in the $L^2$ norm of a given domain. The parallelism between the spaces of contragenic…
We study the convergence of Bernstein type operators leading to two results. The first: The kernel $K_n$ of the Bernstein-Durrmeyer operator at each point $x \in (0, 1)$ $\unicode{x2013}$ that is $K_n(x, t) dt$ $\unicode{x2013}$ once…
Starting with the correspondence between positive definite kernels on the one hand and reproducing kernel Hilbert spaces (RKHSs) on the other, we turn to a detailed analysis of associated measures and Gaussian processes. Point of departure:…
A FORTRAN code for generating the leading SU(3) irreducible representation (irrep) of N identical spin 1/2 fermions in a harmonic oscillator mean field is introduced. The basis states are labeled by N--the total number of particles, the…
Using the generalized Pauli principle by adding particle labels to the usual space and spin labels a symmetric Hamiltonian and a corresponding antisymmetric wavefunction is constructed for systems of three baryons in the strangeness sectors…
A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by…
Paragrassmann algebras are given a sesquilinear form for which one subalgebra becomes a Hilbert space known as the Segal-Bargmann space. This Hilbert space as well as the ambient space of the paragrassmann algebra itself are shown to have…
We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of $\mathscr{L}_2(\mathbb{R})$. This allows us to derive explicit expansions on the real…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…
In \cite{Tre_PSI20} we introduce the concept of a $\mu$-norm for a bounded operator in a Hilbert space. The main motivation is the extension of the measure entropy to the case of quantum systems. In this paper we recall the basic results…
A connection in Kubo-Ando sense is a binary operation for positive operators on a Hilbert space satisfying the monotonicity, the transformer inequality and the continuity from above. A mean is a connection $\sigma$ such that $A \sigma A =A$…
We consider the eigenvalue problem of certain kind of non-compact linear operators given as the sum of a multiplication and a kernel operator. A degenerate kernel method is used to approximate isolated eigenvalues. It is shown that entries…
The notion of a $U$-statistic for an $n$-tuple of identical quantum systems is introduced in analogy to the classical (commutative) case: given a selfadjoint `kernel' $K$ acting on $(\mathbb{C}^{d})^{\otimes r}$ with $r<n$, we define the…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…
This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized…
Various convergence results for the Bergman kernel of the Hilbert space of all polynomials in \C^{n} of total degree at most k, equipped with a weighted norm, are obtained. The weight function is assumed to be C^{1,1}, i.e. it is…