Related papers: On the Hilbert space derived from the Weil distrib…

The primary purpose of the paper is to study how a Riemann mapping depends on the corresponding Jordan curve. We are mainly concerned with those Jordan curves in the Weil-Petersson class, namely, the corresponding Riemann mappings can be…

We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum…

We show that compact Riemannian manifolds, regarded as metric spaces with their global geodesic distance, cannot contain a number of rigid structures such as (a) arbitrarily large regular simplices or (b) arbitrarily long sequences of…

We show that any generalised smooth distribution on a smooth manifold, possibly of non-constant rank, admits a Riemannian metric. Using such a metric, we attach a Laplace operator to any smooth distribution as such. When the underlying…

In this paper, we develop a continual analog of decomposition over orthogonal bases in spaces generated by equidistant shifts of a single function. By doing so, we obtain an explicit expression for best approximation by spaces of shifts in…

We provide explicit commutative sequence space representations for classical function and distribution spaces on the real half-line. This is done by evaluating at the Fourier transforms of the elements of an orthonormal wavelet basis.

We obtain solutions of the Wheeler-DeWitt equation with positive cosmological constant for a closed universe in the large-volume limit. We argue that this space of solutions provides a complete basis for the Hilbert space of quantum gravity…

We study ambiguities in the precise formulation of the Wheeler-DeWitt equation for the wavefunction of the Universe that arise due to different operator orderings in the quantum Hamiltonian. We first examine the simpler case of the…

The stationary reflected Brownian motion in a three-quarter plane has been rarely analyzed in the probabilistic literature, in comparison with the quarter plane analogue model. In this context, our main result is to prove that the…

We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are…

A certain subspace of the Hilbert space of square-integrable functions on the unit interval has been considered by Nyman, Beurling, and others, with the result that the constant function 1 belongs to it if and only if the Riemann Hypothesis…

The purpose of this paper is to prove an interpolation formula involving derivatives for entire functions of exponential type. We extend the interpolation formula derived by J. Vaaler in [37, Theorem 9] to general $L^p$ de Branges spaces.…

This is a survey on a notion of invariant operators, or Fourier multipliers on Hilbert spaces. This concept is defined with respect to a fixed partition of the space into a direct sum of finite dimensional subspaces. In particular this…

We use the theory of pseudo-Hermitian operators to address the problem of the construction and classification of positive-definite invariant inner-products on the space of solutions of a Klein-Gordon type evolution equation. This involves…

We extend some results of M.G. Krein to the class of entire functions which can be represented as ratios of discrete Cauchy transforms in the plane. As an application we obtain new versions of de Branges' Ordering Theorem for nearly…

We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then…

In this article, methods from sub-Hardy Hilbert spaces such as the de Branges-Rovnyak spaces and local Dirichlet spaces are used to investigate B\'aez-Duarte's Hilbert space reformulation of the Riemann hypothesis (RH).

We show that the Hilbert functor of points on an arbitrary separated algebraic stack is an algebraic space. We also show the algebraicity of the Hilbert stack of points on an algebraic stack and the algebraicity of the Weil restriction of…

There has been a surge of interest of late in an old result of Nyman and Beurling giving a Hilbert space formulation of the Riemann hypothesis. Many authors have contributed to this circle of ideas, culminating in a beautiful refinement due…

Consider the (Helgason-) Fourier transform on a Riemannian symmetric space G/K. We give a simple proof of the L^p-Schwartz space isomorphism theorem (0 <p \le 2) for K-finite functions. The proof is a generalization of J.-Ph. Anker's proof…