Related papers: Kernel theorems for modulation spaces
We consider kernels of unbounded Toeplitz operators in $H^p(\mathbb C^+)$ in terms of a factorization of their symbols. We study the existence of a minimal Toeplitz kernel containing a given function in $H^p(\mathbb C^+)$, we describe the…
Feature maps associated with positive definite kernels play a central role in kernel methods and learning theory, where regularity properties such as Lipschitz continuity are closely related to robustness and stability guarantees. Despite…
The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes. Letting a function act by post composition on kernels with arbitrary domains, it is shown…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…
For Schroedinger operators (including those with magnetic fields) with singular (locally integrable) scalar potentials on manifolds of bounded geometry, we study continuity properties of some related integral kernels: the heat kernel, the…
The paper focuses on the behaviour of unimodular Fourier multipliers with exponential growth in the context of weighted $L^p$-spaces. Our main result shows that much of the general theory of multipliers is approachable through the theory of…
If a Banach-space operator has a complemented range, then its normed-space adjoint has a complemented kernel and the converse holds on a reflexive Banach space. It is also shown when complemented kernel for an operator is equivalent to…
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) and that are invariant under actions of $*$-semigroups. For…
The paper extends an earlier result of G.V.~Kalachev and the author (Sb. Math. 2019 or arXiv:1712.08836) on the existence of a maximizer of convolution operator acting between two Lebesgue spaces on $R^n$ with kernel from some $L_q$,…
This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing…
In this paper, we illustrate the effectiveness of reproducing kernel Hilbert space techniques in the study of composition operators. For weighted Hardy spaces on the unit disk, we characterize the composition operators whose adjoint is…
Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and…
In the theory of singular integral operators significant effort is often required to rigorously define such an operator. This is due to the fact that the kernels of such operators are not locally integrable on the diagonal, so the integral…
A well-known theorem due to R. E. Curto and N. Salinas gives a necessary and sufficient condition for the unitary equivalence of commuting tuples of bounded linear operators acting on reproducing kernel Hilbert spaces. Inspired by this…
A now classical result in the theory of variable Lebesgue spaces due to Lerner [A. K. Lerner, On modular inequalities in variable $L^p$ spaces, Archiv der Math. 85 (2005), no. 6, 538-543] is that a modular inequality for the…
This paper considers paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are…
In this paper we have characterized the space of summability kernels for the case p=1 and p=2. For other values of p we give a necessary condition for a function $\Lambda$ to be a summability kernel. For the case p=1, we have studied the…
We prove Beurling's theorem for rank 1 Riemmanian symmetric spaces and relate it to the characterization of the heat kernel of the symmetric space.
Hilbertian kernel methods and their positive semidefinite kernels have been extensively used in various fields of applied mathematics and machine learning, owing to their several equivalent characterizations. We here unveil an analogy with…
Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…