Related papers: Biorthogonal systems on unit interval and zeta dil…

In the present paper I show how it is possible to derive the Hilbert space formulation of Quantum Mechanics from a comprehensive definition of "physical experiment" and assuming "experimental accessibility and simplicity" as specified by…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…

In this paper we formulate a concrete method for determining whether a system of dilated periodic functions forms a Riesz basis in $L^2(0,1)$. This method relies on a general framework developed by Hedenmalm, Lindqvist and Seip about 20…

We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp.…

We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.

A brief non-technical review of the recent study of classical integrable structures in quantum integrable systems is given. It is explained how to identify the standard objects of quantum integrable systems (transfer matrices, Baxter's…

Recently a paper on the construction of consistent Wigner functions for cylindrical phase spaces S^1 x R, i.e. for the canonical pair angle and angular momentum, was presented (arXiv:1601.02520), main properties of those functions derived,…

In this paper we consider evolution equations in the abstract Hilbert space under the special conditions imposed on the operator at the right-hand side of the equation. We establish the method that allows us to formulate the existence and…

In this paper we express some simple random tensor models in a Givental-like fashion i.e. as differential operators acting on a product of generic 1-Hermitian matrix models. Finally we derive Hirota's equations for these tensor models. Our…

Relativistic quantum systems that admit scattering experiments are quantitatively described by effective field theories, where $S$-matrix kinematics and symmetry considerations are encoded in the operator spectrum of the EFT. In this paper…

In this paper, we consider the nonselfadjoint Sturm Liouville operator with and either periodic, or antiperiodic boundary conditions. We obtain necessary and sufficient conditions for systems of root functions of these operators to be a…

This paper explores the domain of meromorphic extension for the dynamical zeta function associated to a class of one-dimensional differentiable parabolic maps featuring an indifferent fixed point. We establish the connection between this…

The complex exponentials with integer frequencies form a basis for the space of square integrable functions on the unit interval. We analyze whether the basis property is maintained if the support of the complex exponentials is restricted…

We consider a family of operators connected with the geodesic flow on the modular surface. We show certain spectral information is retained after expanding their domain to the space of $\alpha$-H\"older continuous functions on the unit…

We present a quantum mechanical model which establishes the veracity of the Riemann hypothesis that the non-trivial zeros of the Riemann zeta-function lie on the critical line of $\zeta(s)$.

A generalization of Mallat's classic theory of multiresolution analysis based on the theory of spectral pairs was considered by Gabardo and Nashed (J. Funct. Anal. 158, 209-241, 1998). In this article, we introduce the notion of…

We suggest an extension of the Hilbert Phase Space formalism, which appears to be naturally suited for application to the dissipative (open) quantum systems, such as those described by the non-stationary (time-dependent) Hamiltonians…

Applying techniques originally developed for systems lacking a variational structure, we establish conditions for the existence of solutions in systems that possess this property but their energy functional is unbounded both lower and…

Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…

We prove certain general forms of functional relations among Witten multiple zeta-functions in several variables (or zeta-functions of root systems). The structural background of those functional relations is given by the symmetry with…