Related papers: Inner functions in reproducing kernel spaces
Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stochastic processes. The first one yields several dilation…
In this paper, we introduce the concept of inner product on weak hypervector spaces and prove some results about them.
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…
Quantum kernels are reproducing kernel functions built using quantum-mechanical principles and are studied with the aim of outperforming their classical counterparts. The enthusiasm for quantum kernel machines has been tempered by recent…
In this paper we investigate the properties of function spaces using the selection principles.
Intrinsic random functions (IRF) provide a versatile approach when the assumption of second-order stationarity is not met. Here, we develop the IRF theory on the circle with its universal kriging application. Unlike IRF in Euclidean spaces,…
This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…
We use the operator method to evaluate a class of integrals involving Bessel or Bessel-type functions. The technique we propose is based on the formal reduction of these family of functions to Gaussians.
The main goal of this paper is to present new bounds for certain inner products in Hilbert spaces, with applications to the numerical radius and the operator norm. The obtained results significantly improve earlier results in this…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
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…
We revisit and connect several notions of algebraic multiplicities of zeros of analytic operator-valued functions and discuss the concept of the index of meromorphic operator-valued functions in complex, separable Hilbert spaces.…
We study Riesz bases/Riesz sequences of reproducing kernels in the model space $K_\theta$ in connection with the corresponding Schur--Nevanlinna parameters and functions. In particular, we construct inner functions with given…
New index transforms, involving the square of Bessel functions of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces.…
We provide a new representation of a refinable shift invariant space with a compactly supported generator, in terms of functions with a special property of homogeneity. In particular these functions include all the homogeneous polynomials…
We present a new operator theoretic framework for analysis of complex systems with intrinsic subdivisions into components, taking the form of "residuals" in general, and "telescoping energy residuals" in particular. We prove new results…
We study mapping properties of operators with kernels defined via a combination of continuous and discrete orthogonal polynomials, which provide an abstract formulation of quantum (q-) Fourier type systems. We prove Ismail conjecture…
The main purpose of this paper is to generalize and develop a few basic properties of the innerproduct space on a hypervector space. On this hypervector space we define the norm. Also we establish a important relation between normed…