Related papers: The polyanalytic reproducing kernels

We deal with a class of one-parameter family of integral transforms of Bargmann type arising as dual transforms of fractional Hankel transform. Their ranges are identified to be special subspaces of the weighted hyperholomorphic left…

We find probability error bounds for approximations of functions $f$ in a separable reproducing kernel Hilbert space $\mathcal{H}$ with reproducing kernel $K$ on a base space $X$, firstly in terms of finite linear combinations of functions…

We analyze the notion of reproducing pair of weakly measurable functions, which generalizes that of continuous frame. We show, in particular, that each reproducing pair generates two Hilbert spaces, conjugate dual to each other. Several…

Let $\nu_{\alpha,q}$ be the probability and orthogonality measure for the $q$-Meixner-Pollaczek orthogonal polynomials, which has appeared in \cite{BEH15} as the distribution of the $(\alpha,q)$-Gaussian process (the Gaussian process of…

This paper deals with some special integral transforms of Bargmann-Fock type in the setting of quaternionic valued slice hyperholomorphic and Cauchy-Fueter regular functions. The construction is based on the well-known Fueter mapping…

We generalize the Beckner's type Poincar\'e inequality \cite{Beckner} to a large class of probability measures on an abstract Wiener space of the form $\mu\star\nu$, where $\mu$ is the reference Gaussian measure and $\nu$ is a probability…

For $0<p,q<\infty$ and $\omega$ a radial weight, the space $L^{p,q}_\omega$ consists of complex-valued measurable functions $f$ on the unit disk such that $$ \| f\|_{L^{p,q}_\omega}^q = \int_0^1 \left…

For the full range of index $0<p\leq\infty$, real weight $\alpha$ and real Sobolev order $s$, two types of weighted Fock-Sobolev spaces over $\mathbb C^n$, $F^p_{\alpha, s}$ and $\widetilde F^p_{\alpha,s}$, are introduced through fractional…

A method for obtaining complex analytic realizations for a class of deformed algebras based on their respective deformation mappings and their ordinary coherent states is introduced. Explicit results of such realizations are provided for…

We count the algebraic numbers of fixed degree by their $\mathbf{w}$-weighted $l_p$-norm which generalizes the na\"ive height, the length, the Euclidean and the Bombieri norms. For non-negative integers $k,l$ such that $k+2l\leq n$ and a…

The Bargmann-Fock space(or Fock space for short) is a fundamental example of reproducing kernel Hilbert spaces that has found fascinating applications across multiple fields of current interest, including quantum mechanics, time-frequency…

We study reproducing kernel Hilbert spaces introduced as ranges of generalized Ces\`aro-Hardy operators, in one real variable and in one complex variable. Such spaces can be seen as formed by absolutely continuous functions on the positive…

Let $\lambda$ be a general length function for modules over a Noetherian ring R. We use $\lambda$ to introduce Hilbert series and polynomials for R[X]-modules, measuring the growth rate of~$\lambda$. We show that the leading term $\mu$ of…

We provide a complete characterization of compactness of Sobolev embeddings of radially symmetric functions on the entire space $\mathbb{R}^n$ in the general framework of rearrangement-invariant function spaces. We avoid any unnecessary…

A Hilbert space embedding for probability measures has recently been proposed, wherein any probability measure is represented as a mean element in a reproducing kernel Hilbert space (RKHS). Such an embedding has found applications in…

We generalise the result of Berger and Shaw the trace formula for Hardy Hilbert space to a larger class of rotation invariant Hilbert function spaces on the unit disk. We also demonstrate many meaningful examples of these Hilbert spaces by…

The local kinematic formulas on complex space forms induce the structure of a commutative algebra on the space $\mathrm{Curv}^{\mathrm{U}(n)*}$ of dual unitarily invariant curvature measures. Building on the recent results from integral…

The aim of the present paper is three folds. For a reproducing kernel Hilbert space $\mathcal{A}$ (R.K.H.S) and a $\sigma-$finite measure space $(M_{1},d\mu_{1})$ for which the corresponding $L^{2}-$space is a separable Hilbert space, we…

While finite non-commutative operator systems lie at the foundation of quantum measurement, they are also tools for understanding geometric iterations as used in the theory of iterated function systems (IFSs) and in wavelet analysis. Key is…

Let $\mu$ be a positive Borel measure on the interval $[0,1)$. For $\alpha>0$, the generalized Hankel matrix $\mathcal{H}_{\mu, \alpha}=(\mu_{n, k, \alpha})_{n, k \geq 0}$ with entries $\mu_{n, k, \alpha}=\int_{[0,1)}…