Generalized Moment Functions and Orbit Spaces

AbstractThe purpose of this paper is to prove that if on a commutative hypergroup an exponential monomial has the property that the linear subspace of all sine functions in its variety is one dimensional, then this exponential monomial is a linear combination of generalized moment functions.

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Moment functions on hypergroup joins

Advances in Pure and Applied Mathematics ◽

10.1515/apam-2018-0027 ◽

2019 ◽

Vol 10 (3) ◽

pp. 215-220

Author(s):

Kedumetse Vati ◽

László Székelyhidi

Keyword(s):

Probability Theory ◽

Functional Equations ◽

Spectral Synthesis ◽

Natural Generalization ◽

Moment Function ◽

Function Classes ◽

Moment Functions ◽

Basic Blocks ◽

Generalized Moment

Abstract Moment functions play a basic role in probability theory. A natural generalization can be defined on hypergroups which leads to the concept of generalized moment function sequences. In a former paper we studied some function classes on hypergroup joins which play a basic role in spectral synthesis. Moment functions are also important basic blocks of spectral synthesis. All these functions can be characterized by well-known functional equations. In this paper we describe generalized moment function sequences on hypergroup joins.

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Moment Functions on Groups

Results in Mathematics ◽

10.1007/s00025-021-01467-6 ◽

2021 ◽

Vol 76 (4) ◽

Author(s):

Żywilla Fechner ◽

Eszter Gselmann ◽

László Székelyhidi

Keyword(s):

Commutative Group ◽

Bell Polynomials ◽

Exponential Polynomials ◽

Bell Polynomial ◽

Rank One ◽

Moment Functions ◽

Binomial Type ◽

Higher Rank ◽

Generalized Moment

AbstractIn this paper generalized moment functions are considered. They are closely related to the well-known functions of binomial type which have been investigated on various abstract structures. The main purpose of this work is to prove characterization theorems for generalized moment functions on commutative groups. At the beginning a multivariate characterization of moment functions defined on a commutative group is given. Next the notion of generalized moment functions of higher rank is introduced and some basic properties on groups are listed. The characterization of exponential polynomials by means of complete (exponential) Bell polynomials is given. The main result is the description of generalized moment functions of higher rank defined on a commutative group as the product of an exponential and composition of multivariate Bell polynomial and an additive function. Furthermore, corollaries for generalized moment function of rank one are also stated. At the end of the paper some possible directions of further research are discussed.

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The generalized moment method for analysis of structures with varying feature sizes

2nd European Conference on Antennas and Propagation (EuCAP 2007) ◽

10.1049/ic.2007.1285 ◽

2007 ◽

Author(s):

N.V. Nair ◽

M. Vikram ◽

B. Shanker ◽

L.C. Kempel

Keyword(s):

Moment Method ◽

Generalized Moment

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On the sufficiency of K-positivity for truncated, compactly supported, generalized moment problems

Examples and Counterexamples ◽

10.1016/j.exco.2021.100006 ◽

2021 ◽

pp. 100006

Author(s):

Axel Ringh

Keyword(s):

Moment Problems ◽

Compactly Supported ◽

Generalized Moment

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FAST COMPUTATION OF GEOMETRIC MOMENTS AND INVARIANTS USING SCHLICK'S APPROXIMATION

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001408006764 ◽

2008 ◽

Vol 22 (07) ◽

pp. 1363-1377 ◽

Cited By ~ 3

Author(s):

R. MUKUNDAN

Keyword(s):

Fast Computation ◽

Recent Past ◽

Computational Overhead ◽

Geometric Moments ◽

Alternative Approach ◽

Computational Speed ◽

Moment Functions ◽

The Moment ◽

Moment Integral ◽

Modified Moments

Geometric moments have been used in several applications in the field of Computer Vision. Many techniques for fast computation of geometric moments have therefore been proposed in the recent past, but these algorithms mainly rely on properties of the moment integral such as piecewise differentiability and separability. This paper explores an alternative approach to approximating the moment kernel itself in order to get a notable improvement in computational speed. Using Schlick's approximation for the normalized kernel of geometric moments, the computational overhead could be significantly reduced and numerical stability increased. The paper also analyses the properties of the modified moment functions, and shows that the proposed method could be effectively used in all applications where normalized Cartesian moment kernels are used. Several experimental results showing the invariant characteristics of the modified moments are also presented.

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