Approximation Theorems Associated with Multidimensional Fractional Fourier Transform and Applications in Laplace and Heat Equations
Yinuo Yang, Qingyan Wu, Seong Tae Jhang, Qianqian Kang
Abstract
In this paper, we establish two approximation theorems for the multidimensional fractional Fourier transform via appropriate convolutions. As applications, we study the boundary and initial problems of the Laplace and heat equations with chirp functions. Furthermore, we obtain the general Heisenberg inequality with respect to the multidimensional fractional Fourier transform.
Topics & Concepts
MathematicsLaplace transformFractional Fourier transformFourier transformMathematical analysisLaplace transform applied to differential equationsHeat equationFourier inversion theoremFractional calculusTwo-sided Laplace transformApplied mathematicsFourier analysisMathematical Analysis and Transform MethodsImage and Signal Denoising MethodsAdvanced Harmonic Analysis Research