Related papers: The Corona Problem for Kernel Multiplier Algebras
We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest,…
We develop a structural classification of multipliers between generalized Toeplitz kernels, extending the work of Fricain and Rupam. Our results establish new equivalences between multiplier space and Carleson-type embeddings, linking them…
We introduce the notion of a pseudomultiplier of a Hilbert space $\mathcal H$ of functions on a set $\Omega$. Roughly, a pseudomultiplier of $\mathcal H$ is a function which multiplies a finite-codimensional subspace of $\mathcal H$ into…
We introduce Besov and Triebel--Lizorkin spaces on a manifold with boundary adapted to H\"ormander vector fields, near a so-called non-characteristic point of the boundary. We prove sharp results in these spaces for the corresponding…
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…
Kernel interpolation in tensor product reproducing kernel Hilbert spaces allows for the use of sparse grids to mitigate the curse of the dimension. Typically, besides the generic constant, only a dimension dependent power of a logarithm…
We obtain kernel functions associated with the quantum relativistic Toda systems, both for the periodic version and for the nonperiodic version with its dual. This involves taking limits of previously known results concerning kernel…
We study the cyclicity of multipliers in Dirichlet-type spaces \( D_\alpha(\mathbb{B}_n) \). Specifically, we show that a multiplier \( f \) analytic on a neighborhood of $\overline{\mathbb{B}}_n$, whose zero set on the unit sphere is a…
It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in…
We establish some basic theorems in dimension theory and absolute extensor theory in the coarse category of metric spaces. Some of the statements in this category can be translated in general topology language by applying the Higson corona…
We study the multiplier algebras $A(\mathcal{H})$ obtained as the closure of the polynomials on certain reproducing kernel Hilbert spaces $\mathcal{H}$ on the ball $\mathbb{B}_d$ of $\mathbb{C}^d$. Our results apply, in particular, to the…
We prove stronger variants of a multiplier theorem of Kislyakov. The key ingredients are based on ideas of Kislaykov and the Kahane-Salem-Zygmund inequality. As a by-product we show various multiplier theorems for spaces of trigonometric…
Toeplitz operators are met in different fields of mathematics such as stochastic processes, signal theory, completeness problems, operator theory, etc. In applications, spectral and mapping properties are of particular interest. In this…
We demonstrate that a reproducing kernel Hilbert or Banach space of functions on a separable absolute Borel space or an analytic subset of a Polish space is separable if it possesses a Borel measurable feature map.
We investigate the Schwarz lemma and the Schur algorithm for elements in the unit ball of the multiplier algebra of a reproducing kernel Hilbert space on the open unit ball whose kernel satisfies the complete Nevanlinna-Pick property. This…
We prove that the homogeneously polyanalytic functions of total order $m$, defined by the system of equations $\overline{D}^{(k_1,\ldots,k_n)} f=0$ with $k_1+\cdots+k_n=m$, can be written as polynomials of total degree $<m$ in variables…
In this paper we study the kernels of Toeplitz operators on both the scalar and the vector-valued Hardy space for $ 1 < p < \infty $. We show existence of a minimal kernel of any element of the vector-valued Hardy space and we determine a…
We raise a conjecture that asymptotics for Chebyshev polynomials in a complex domain can be given in terms of the reproducing kernels of a suitable Hilbert space of analytic functions in this domain. It is based on two classical results due…
In the paper we study the multipliers of Fourier series in polynomials orthogonal in continuous-discrete Sobolev's spaces. Multiplier Theorem for Fourier-Sobolev series is obtained. This result is based on the representation of the Fej\'er…
Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…