Related papers: Laplace transforms and valuations
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization,…
A representation theorem for continuous, SL(n) covariant vector-valued valuations on Orlicz spaces is established. Such valuations are uniquely characterized as moment vectors.
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of…
We give a novel descriptive-complexity theoretic characterization of L and NL computable queries over finite structures using traversal invariance. We summarize this as (N)L = FO + (breadth-first) traversal-invariance.
In this paper, we present a new derivative via the Laplace transform. The Laplace transform leads to a natural form of the fractional derivative which is equivalent to a Riemann-Liouville derivative with fixed terminal point. We first…
The harmonic chain is a classical many-particle system which can be solved exactly for arbitrary number of particles (at least in simple cases, such as equal masses and spring constants). A nice feature of the harmonic chain is that the…
We obtain necessary and sufficient conditions on a function in order that it be the Laplace transform of an absolutely monotonic function. Several closely related results are also given.
We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.
The functions studied in the paper are quaternion-valued functions of a quaternionic variable. It is show that the left slice regular functions and right slice regular functions are related by a particular involution. The relation between…
In this paper, we introduce the degenerate Laplace transform and degenerate gamma function and investigate some properties of the degenerate Laplace transform and degenerate gamma function. From our investigation, we derive some interesting…
In this paper, we consider a q-analogue of Laplace transform and we investigate some properties of q-Laplace transform. From our investigation, we derive some interesting formulae related to q-Laplace transform.
We study real-valued, continuous and translation invariant valuations defined on the space of quasi-concave functions of N variables. In particular, we prove a homogeneous decomposition theorem of McMullen type, and we find a representation…
Translation-invariant valuations on the space $L^\infty(\mathbb{R}^n)$ are examined. We prove that such functionals vanish on functions with compact support. Moreover a rich family of non-trivial translation-invariant valuations on…
Let $\mathrm{SO}^+(p,q)$ denote the identity connected component of the real orthogonal group with signature $(p,q)$. We give a complete description of the spaces of continuous and generalized translation- and $\mathrm{SO}^+(p,q)$-invariant…
The Laplace transform in Komatsu ultradistributions is considered. Also, conditions are given under which an analytic function is a Laplace transformation of an ultradistribution.
Landen transformations are maps on the coefficients of an integral that preserve its value. We present a brief survey of their appearnce in the literature.
Alesker has proved the existence of a remarkable isomorphism of the space of translation-invariant smooth valuations that has the same functorial properties as the classical Fourier transform. In this paper, we show how to directly describe…
Let $G(g;x):=\sum_{n\leq x}g(n)$ be the summatory function of an arithmetical function $g(n)$. In this paper, we prove that we can write weighted averages of an arbitrary fixed number $N$ of arithmetical functions $g_{j}(n),\,j\in\left\{…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
The one-dimensional quantum harmonic oscillator problem is examined via the Laplace transform method. The stationary states are determined by requiring definite parity and good behaviour of the eigenfunction at the origin and at infinity.