Название: Analysis, Geometry, Nonlinear Optimization and Applications
Автор: Panos M Pardalos, Themistocles M. Rassias
Издательство: World Scientific Publishing
Серия: Series on Computers and Operations Research
Год: 2023
Страниц: 895
Язык: английский
Формат: pdf (true)
Размер: 17.7 MB

This volume features an extensive account of both research and expository papers in a wide area of engineering and mathematics and its various applications.Topics treated within this book include optimization of control points, game theory, equilibrium points, algorithms, Cartan matrices, integral inequalities, Volterra integro-differential equations, Caristi-Kirk theorems, Laplace type integral operators, etc. This useful reference text benefits graduate students, beginning research engineers and mathematicians as well as established researchers in these domains.

In this chapter, we define the quaternionic fractional Fourier transform and study some of its properties like Riemann–Lebesgue lemma, Parseval’s formula and convolution theorem. We also define the fractional wavelet transform of the quaternionic valued function and obtain its basic properties, the inner product relation, inversion formula and the range of the transform. We derive Heisenberg’s uncertainty principle for the quaternionic fractional Fourier transform, which enables us to derive also Heisenberg’s uncertainty principle for the quaternionic fractional wavelet transform.