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We consider the $m$-dimensional modified Helmholtz equation and establish two relations between its solutions in a bounded domain and harmonic functions. Both relations essentially rely on properties of the Newtonian potential. Some other…
Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional…
The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of…
We show a simple mechanism to measure the Wigner function of a harmonic oscillator. For this system we also show that autocorrelation and Wigner functions are equivalent.
The goal of this note is to extend the result bounding from bellow the minimal possible growth of frequently oscillating subharmonic functions to a larger class of functions that carry similar properties. We refine and find further…
In this paper, we study some properties such as the monotonicity, logarithmically complete monotonicity, logarithmic convexity, and geometric convexity, of the combinations of gamma function and power function. The results we obtain…
A universal differential equation is a nontrivial differential equation the solutions of which approximate to arbitrary accuracy any continuous function on any interval of the real line. On the other hand, there has been much interest in…
A positive correlation inequality is established for circular-invariant plurisubharmonic functions, with respect to complex Gaussian measures. The main ingredients of the proofs are the Ornstein-Uhlenbeck semigroup, and another natural…
The paper addresses the calculation of correlation functions of permanental polynomials of matrices with random entries. By exploiting a convenient contour integral representation of the matrix permanent some explicit results are provided…
In this papaer, we put forward some new definitions and integral inequalities by using fairly elementary analysis.
Gauge-fixed correlation functions are a valuable tool in intermediate steps when determining gauge-invariant physics. However, when obtaining them in different calculations, it is necessary to use exactly the same definition of the gauge to…
A Choquet-type integral representation result for non-negative subharmonic functions of a one-dimensional regular diffusion is established. The representation allows in particular an integral equation for strictly positive subharmonic…
A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…
We study the Schwarz lemma for harmonic functions and prove sharp versions for the cases of real harmonic functions and the norm of harmonic mappings.
Discrete interaction models for the classical harmonic oscillator are used for introducing new mathematical generalizations in the usual continuous formalism. The inverted harmonic potential and generalized discrete hyperbolic and…
The aim of this paper is to establish properties of the solutions to the $\alpha$-harmonic equations: $\Delta_{\alpha}(f(z))=\partial{z}[(1-{|{z}|}^{2})^{-\alpha} \overline{\partial}{z}f](z)=g(z)$, where…
We briefly describe some well-known means and their properties, focusing on the relationship with integer sequences. In particular, the harmonic numbers, deriving from the harmonic mean, motivate the definition of a new kind of mean that we…
We present in this paper the motivation and theory of nonlinear spectral representations, based on convex regularizing functionals. Some comparisons and analogies are drawn to the fields of signal processing, harmonic analysis and sparse…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…