Related papers: Spectral Analysis of the local Conductor Operator

We study a fractional differentiation operator for functions on the conjugate space to an infinite extension of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. In particular, a…

The aim of this article is to explore in all remaining aspects the spectral theory of locally normal operators. In a previous article we proved the spectral theorem in terms of locally spectral measures. Here we prove the spectral theorem…

A modified Green operator is proposed as an improvement of Fourier-based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media. Contrary to other methods, the number of iterations necessary…

We establish the Fourier inversion for the smooth vectors in ${\rm L}^2({\rm GL}_2, \omega)$ over a number field $\mathbf{F}$, using minimal knowledge from automorphic representation theory. We point out a possible way to establish Fourier…

We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite von Neumann algebras we give applications to the Fr\'echet…

We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density…

Conformal theory correlators are characterized by the spectrum and three- point functions of local operators. We present a formula which extracts this data as an analytic function of spin. In analogy with a classic formula due to Froissart…

In this paper it is shown that a function of the constant dot product of the gradient operator acting on an arbitrary function can be transformed to a double three-dimensional integral. The inner one of them is a Fourier transform of the…

The classical Fourier transform on the line sends the operator of multiplication by $x$ to $i\frac{d}{d\xi}$ and the operator of differentiation $\frac{d}{d x}$ to the multiplication by $-i\xi$. For the Fourier transform on the Lobachevsky…

For a split reductive group $G$ over a number field $k$, let $\rho$ be an $n$-dimensional complex representation of its complex dual group $G^\vee(\mathbb{C})$. For any irreducible cuspidal automorphic representation $\sigma$ of…

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…

In this paper, we explore a possibility to utilize harmonic analysis on $\GL_1$ to understand Langlands automorphic $L$-functions in general, as a vast generalization of the pioneering work of J. Tate. For a split reductive group $G$ over a…

The bispectral problem is motivated by an effort to understand and extend a remarkable phenomenon in Fourier analysis on the real line: the operator of time-and-band limiting is an integral operator admitting a second-order differential…

The recently introduced concept of a spectral shift operator is applied in several instances. Explicit applications include Krein's trace formula for pairs of self-adjoint operators, the Birman-Solomyak spectral averaging formula and its…

We consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on…

Inverse spectral problem for a self-adjoint differential operator, which is the sum of the operator of the third derivative on a finite interval and of the operator of multiplication by a real function (potential), is solved. Closed system…

A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of…

In this note, we deal with the fractional Logarithmic Schr\"{o}dinger operator $(I+(-\Delta)^s)^{\log}$ and the corresponding energy spaces for variational study. The fractional (relativistic) Logarithmic Schr\"{o}dinger operator is the…

In this paper presents the results obtained in the field of spectral theory operators of fractional differentiation. Proven a number of propositions which represents independent interest in the theory of fractional calculus. Introduced…

This paper is the continuation of our work with Victor Guillemin; Victor and I proved that the Taylor expansion of the potential at a generic non degenerate critical point is determined by the semi-classical spectrum of the associated…