scholarly journals Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres

2019 ◽  
Vol 294 (3-4) ◽  
pp. 1659-1686
Author(s):  
Julian Ahrens ◽  
Michael G. Cowling ◽  
Alessio Martini ◽  
Detlef Müller
Keyword(s):  
Spherical Harmonics ◽  
Multiplier Theorem

scholarly journals From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere

2019 ◽  
Vol 350 ◽  
pp. 816-859 ◽  
Author(s):  
Valentina Casarino ◽  
Paolo Ciatti ◽  
Alessio Martini
Keyword(s):  
Spherical Harmonics ◽  
Multiplier Theorem

Zonal and tesseral harmonic perturbations of an artificial satellite

1966 ◽  
Vol 25 ◽  
pp. 323-325 ◽  
Author(s):  
B. Garfinkel
Keyword(s):  
Angular Velocity ◽  
Spherical Harmonics ◽  
Artificial Satellite ◽  
Compact Form ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Secular Variations ◽  
Tesseral Harmonics

The paper extends the known solution of the Main Problem to include the effects of the higher spherical harmonics of the geopotential. The von Zeipel method is used to calculate the secular variations of orderJmand the long-periodic variations of ordersJm/J2andnJm,λ/ω. HereJmandJm,λare the coefficients of the zonal and the tesseral harmonics respectively, withJm,0=Jm, andωis the angular velocity of the Earth's rotation. With the aid of the theory of spherical harmonics the results are expressed in a most compact form.

Nearly spherical vesicle shapes calculated by use of spherical harmonics : axisymmetric and nonaxisymmetric shapes and their stability

1992 ◽  
Vol 2 (5) ◽  
pp. 1081-1108 ◽  
Author(s):  
V. Heinrich ◽  
M. Brumen ◽  
R. Heinrich ◽  
S. Svetina ◽  
B. Žekš
Keyword(s):  
Spherical Harmonics ◽  
Spherical Vesicle ◽  
Vesicle Shapes

A new insight and improvement on deconvolution beamforming in spherical harmonics domain

2021 ◽  
Vol 177 ◽  
pp. 107900
Author(s):  
Zhigang Chu ◽  
Yongxin Yang ◽  
Yang Yang
Keyword(s):  
Spherical Harmonics

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

Applications of Erdélyi-Kober fractional integral for solving time-fractional Tricomi-Keldysh type equation

2020 ◽  
Vol 23 (5) ◽  
pp. 1381-1400 ◽  
Author(s):  
Kangqun Zhang
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Integral Operator ◽  
Nonlinear Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Formal Solution ◽  
Type Equation ◽  
Multiplier Theorem ◽  
Problem Of Time

Abstract In this paper we consider Cauchy problem of time-fractional Tricomi-Keldysh type equation. Based on the theory of a Erdélyi-Kober fractional integral operator, the formal solution of the inhomogeneous differential equation involving hyper-Bessel operator is presented with Mittag-Leffler function, then nonlinear equations are considered by applying Gronwall-type inequalities. At last, we establish the existence and uniqueness of L p -solution of time-fractional Tricomi-Keldysh type equation by use of Mikhlin multiplier theorem.

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