Related papers: Fractional Differentiation Operator over an Infini…

The Mittag-Leffler function $E_{\alpha}$ being a natural generalization of the exponential function, an infinite-dimensional version of the fractional Poisson measure would have a characteristic functional \[ C_{\alpha}(\phi)…

A derivative expansion technique is developed to compute functional determinants of quadratic operators, non diagonal in spacetime indices. This kind of operators arise in general 't Hooft gauge fixed Lagrangians. Elaborate applications of…

In this paper we consider an alternative orthogonal decomposition of the space $L^2$ associated to the $d$-dimensional Jacobi measure and obtain an analogous result to P.A. Meyer's Multipliers Theorem for d-dimensional Jacobi expansions.…

Finite rank point perturbations of the $p$-adic fractional differentiation operator $D^{\alpha}$ are studied. The main attention is paid to the description of operator realizations (in $L_2(\mathbb{Q}_p)$) of the heuristic expression…

We study the existence of global weak solutions of a nonlinear transport-diffusion equation with a fractional derivative in the time variable and under some extra hypotheses, we also study some regularity properties for this type of…

Ruelle's transfer operator plays an important role in understanding thermodynamic and probabilistic properties of dynamical systems. In this work, we develop a method of finding eigenfunctions of transfer operators based on comparing Gibbs…

Global conformal invariance determines the form of two and three-point functions of quasi-primary operators in a conformal field theory, and generates nontrivial relations between terms in the operator product expansion. These ideas are…

Let $U$ be a unitary operator defined on some infinite-dimensional complex Hilbert space ${\cal H}$. Under some suitable regularity assumptions, it is known that a local positive commutation relation between $U$ and an auxiliary…

In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…

For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of the operator theory in fractional Sobolev spaces. Our framework provides a feasible extension of the classical Caputo and the…

This work is concerned with fractional Gaussian fields, i.e. Gaussian fields whose covariance operator is given by the inverse fractional Laplacian $(-\Delta)^{-s}$ (where, in particular, we include the case $s >1$). We define a lattice…

Regression on function spaces is typically limited to models with Gaussian process priors. We introduce the notion of universal functional regression, in which we aim to learn a prior distribution over non-Gaussian function spaces that…

We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then…

The fractional moment method, which was initially developed in the discrete context for the analysis of the localization properties of lattice random operators, is extended to apply to random Schr\"odinger operators in the continuum. One of…

Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a…

In this paper we introduce the notion of fractional martingale as the fractional derivative of order $\alpha$ of a continuous local martingale, where $\alpha\in(-{1/2},{1/2})$, and we show that it has a nonzero finite variation of order…

Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…

The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus…

We introduce the concept of a \mu-scale invariant operator with respect to unitary transformation in a separable complex Hilbert space. We show that if a nonnegative densely defined symmetric operator is \mu-scale invariant for some \mu >0,…

We consider a "superposition operator" obtained through the continuous superposition of operators of mixed fractional order, modulated by a signed Borel finite measure defined over the set $[0, 1]$. The relevance of this operator is rooted…