Related papers: Inner functions in reproducing kernel spaces
We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.
We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.
Let $T$ be an absolutely continuous polynomially bounded operator, and let $\theta$ be a singular inner function. It is shown that if $\theta(T)$ is invertible and some additional conditions are fulfilled, then $T$ has nontrivial…
In this note, we compute the reproducing kernel for the RKHS of functions on $\mathbb{R}^n$ in a sufficiently high Sobolev norm.
We introduce a vector differential operator $\mathbf{P}$ and a vector boundary operator $\mathbf{B}$ to derive a reproducing kernel along with its associated Hilbert space which is shown to be embedded in a classical Sobolev space. This…
The set of effect operators in a complex Hilbert space can be injectively embedded into the set of functions from the set of one-dimensional projections to the real interval [0,1]. Properties of this injection are investigated.
Integral transforms $$(\mbox{\boldmath$H$}f)(x)=\int^\infty_0H^{m,n}_{\thinspace p,q} \left[xt\left|\begin{array}{c}(a_i,\alpha_i)_{1,p}\\[1mm](b_j,\beta_j)_{1,q} \end{array}\right.\right]f(t)dt$$ involving Fox's $H$-functions as kernels…
We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…
We discuss when an operator, subject to a rather general inequality in hereditary form, admits a unitarily equivalent functional model of Agler type in the reproducing kernel Hilbert space associated to the inequality. To the contrary to…
A family of partial functions of a class of algebras $\mathsf{K}$ is said to be an implicit operation of $\mathsf{K}$ when it is defined by a first order formula and it is preserved by homomorphisms. In this work, we develop the theory of…
We consider the classical dynamics given by a one sided shift on the Bernoulli space of $d$ symbols. We study, on the space of H\"older functions, the eigendistributions of the Ruelle operator with a given potential. Our main theorem shows…
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…
The concept of intrinsic and operational observables in quantum mechanics is introduced. In any realistic description of a quantum measurement that includes a macroscopic detecting device, it is possible to construct from the statistics of…
A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem…
Function encoders are a recent technique that learn neural network basis functions to form compact, adaptive representations of Hilbert spaces of functions. We show that function encoders provide a principled connection to feature learning…
Lecture note topics: 1. Some tools from real and complex analysis, 2. Hilbert spaces, 3. Banach spaces, 4. Compact operators and their spectra, 5. Intermezzo: reproducing kernel Hilbert spaces, 6. Banach algebras ,7. Spectral theory of…
In this paper we consider the problem of approximating vector-valued functions over a domain $\Omega$. For this purpose, we use matrix-valued reproducing kernels, which can be related to Reproducing kernel Hilbert spaces of vectorial…
Recently some Mathematician extend the notion of Baire one functions. We give some nice relations between this subring and some nice functions rings on a topological spaces.
The objective of this paper is to study wandering subspaces for commuting tuples of bounded operators on Hilbert spaces. It is shown that, for a large class of analytic functional Hilbert spaces $\mathcal{H}_K$ on the unit ball in $\mathbb…