相关论文: On the completeness of Gaussians in a Hilbert func…

In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.

The mathematical description of the quantum harmonic oscillator is essentially based on the Gaussian function. In the case of a quantum oscillator with finite-dimensional Hilbert space, the position space consists in a finite number of…

We prove that any complete metric space has a unique decomposition as a direct product of a possibly finite or zero-dimensional Hilbert space and a space that does not split off lines.

We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable…

We introduce and study the Steiner entire function, an analytic generating function for the intrinsic volumes of a convex compact set in a Hilbert space. This function extends the classical Steiner polynomial to infinite dimensions and…

We study the Hilbert space obtained by completing the space of all smooth and compactly supported functions on the real line with respect to the hermitian form arising from the Weil distribution under the Riemann hypothesis. It turns out…

The Minimal Euclidean Function on the Gaussian Integers

Gel'fand triples of test and generalized functionals in Gaussian spaces are constructed and characterized.

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

Criteria and constructive methods for the completion of an incomplete basis of, or context in, a four-dimensional Hilbert space by (in)decomposable vectors are given.

Linear filtering problem for infinite-dimensional Gaussian processes is studied, the observation process being finite-dimensional. Integral equations for the filter and for covariance of the error are derived. General results are applied to…

Let $H$ be a Hilbert space of entire functions. Let $H'$ be the space of the functions $f(z)/\prod_i(z-z_i)$ where $f$ belongs to $H$ and vanishes at $n$ given complex points $z_i$. We compute a suitable $E$ function for $H'$ when one is…

In this paper we analyse the structure of the spaces of smooth type functions, generated by elements of arbitrary Hilbert spaces, as a continuation of the research in our previous papers in this series. We prove that these spaces are…

This work presents problems of constructing finite-difference formulas in the Hilbert space, i.e., setting problems of constructing finite-difference formulas using functional methods. The work presents a functional statement of the problem…

In this paper, we aim to obtain a representation of Humbert's hy- pergeometric function in a series of Gauss's function 2F1. A few interesting results have also been deduced as special case of our main findings.

We give necessary and sufficient conditions for the sum of n subspaces of a Hilbert space to be closed. We also present various properties of n-tuples of subspaces with closed sum.

This paper describes the concepts of Universal/ Integrally Strictly Positive Definite/ $C_{0}$-Universal for the Gaussian kernel on a Hilbert space. As a consequence we obtain a similar characterization for an important family of kernels…

We investigate an extended version of Hilbert space of analytic functions called Hilbert space of complex-valued harmonic functions. It is found that functions in Hilbert space of complex-valued harmonic functions exhibit many properties…

Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…

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…