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Related papers: Fundamental Solutions for the Tricomi Operator, II

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Due to the isotropy of $d$-dimensional hyperbolic space, one expects there to exist a spherically symmetric fundamental solution for its corresponding Laplace-Beltrami operator. The $R$-radius hyperboloid model of hyperbolic geometry…

Mathematical Physics · Physics 2012-01-24 Howard S. Cohl , Ernie G. Kalnins

For weighted Toeplitz operators $\T^N_\phi$ defined on spaces of holomorphic functions in the unit ball, we derive regularity properties of the solutions $f$ to the integral equation $\T^N_\phi(f)=h$ in terms of the regularity of the symbol…

Complex Variables · Mathematics 2010-09-17 Carme Cascante , Joan Fabrega , Daniel Pascuas

By making use of some techniques based upon certain inverse new pairs of symbolic operators, the author investigate several decomposition formulas associated with Humbert hypergeometric functions $\Phi_1 $, $\Phi_2 $, $\Phi_3 $, $\Psi_1 $,…

Mathematical Physics · Physics 2008-10-22 A. Hasanov

We solve connection problem between fundamental solutions at singular points $0$ and $1$ for the generalized hypergeometric function, using analytic continuation of the integral representation. All connection coefficients are products of…

Classical Analysis and ODEs · Mathematics 2019-04-08 Y. Matsuhira , H. Nagoya

In investigation of boundary-value problems for certain partial differential equations arising in applied mathematics, we often need to study the solution of system of partial differential equations satisfied by hypergeometric functions and…

Classical Analysis and ODEs · Mathematics 2014-01-28 Maged G. Bin-Saad , Anvar Hasanov

We present some integral transform that allows to obtain solutions of the generalized Tricomi equation from solutions of a simpler equation. We used in [13,14],[41]-[46] the particular version of this transform in order to investigate in a…

Analysis of PDEs · Mathematics 2015-04-21 Karen Yagdjian

With the help of some techniques based on certain inverse pairs of symbolic operators, the authors investigated several decomposition formulas associated with Srivastava's Hypergeometric functions of three variables. Some operator…

Analysis of PDEs · Mathematics 2015-09-22 Anvar H. Hasanov , Rakhila B. Seilkhanova , Roza D. Seilova

We develop basic properties of solutions to the Dirac-Hodge and Laplace equations in upper half space endowed with the hyperbolic metric. Solutions to the Dirac-Hodge equation are called hypermonogenic functions while solutions to this…

Analysis of PDEs · Mathematics 2016-09-07 Yuying Qiao , Swanhild Bernstein , Sirkka-Liisa Eriksson , John Ryan

We construct homotopy formulae $f=\overline\partial \mathcal H_q f+\mathcal H_{q+1}\overline\partial f$ on a bounded domain which is either $C^2$ strongly pseudoconvex or $C^{1,1}$ strongly $\mathbb C$-linearly convex. Such operators…

Complex Variables · Mathematics 2024-12-31 Liding Yao

In this note, we construct an algorithm that, on input of a description of a structurally stable planar dynamical flow $f$ defined on the closed unit disk, outputs the exact number of the (hyperbolic) equilibrium points and their locations…

Logic · Mathematics 2021-10-01 Daniel S. Graça , Ning Zhong

In this article, we prove an existence theorem regarding the weak solutions to the hyperbolic-type partial dynamic equation \begin{equation*}\begin{array}{l} z^{\Gamma\Delta}(x,y)=f(x, y, z(x, y)), z(x, 0)=0, \ \ \ z(0, y)=0 \end{array}, \…

Analysis of PDEs · Mathematics 2014-12-24 Ahmet Yantir , Duygu Soyoglu

We principally present reductions of certain generalized hypergeometric functions $_3F_2(\pm 1)$ in terms of products of elementary functions. Most of these results have been known for some time, but one of the methods, wherein we…

Classical Analysis and ODEs · Mathematics 2015-07-01 Mark W. Coffey

The objective of this short note is to provide two closed-form evaluations for the generalized hypergeometric function $_4F_3$ of the argument $\frac1{16}$. This is achieved by means of separating a generalized hypergeometric function…

Classical Analysis and ODEs · Mathematics 2025-01-14 Arjun K. Rathie , Mykola A. Shpot

Topological 1-soliton solutions to various conformable fractional PDEs in both one and more dimensions are constructed by using simple hyperbolic function ansatz. Suitable traveling wave transformation reduces the fractional partial…

Exactly Solvable and Integrable Systems · Physics 2017-09-11 Gokhan Koyunlu

We give an analogy of Jacobi's formula, which relates the hypergeometric function with parameters $(1/4,1/4,1)$ and theta constants. By using this analogy and twice formulas of theta constants, we obtain a transformation formula for this…

Classical Analysis and ODEs · Mathematics 2022-02-25 Jun Chiba , Keiji Matsumoto

We study effectively hyperbolic operators $P$ with triple characteristics points lying on $t= 0$. Under some conditions on the principal symbol of $P$ one proves that the Cauchy problem for $P$ in $[0, T] \times U$ is well posed for every…

Analysis of PDEs · Mathematics 2018-12-11 Tatsuo Nishitani , Vesselin Petkov

We study existence, uniqueness, and distributional aspects of generalized solutions to the Cauchy problem for first-order symmetric (or Hermitian) hyperbolic systems of partial differential equations with Colombeau generalized functions as…

Analysis of PDEs · Mathematics 2011-11-10 Guenther Hoermann , Christian Spreitzer

We give a factorization procedure for a strictly hyperbolic partial differential operator of second order with logarithmic slow scale coefficients. From this we can microlocally diagonalize the full wave operator which results in a coupled…

Analysis of PDEs · Mathematics 2017-06-27 Martina Glogowatz

In this paper we establish optimal local and global Besov-Lipschitz and Triebel-Lizorkin estimates for the solutions to linear hyperbolic partial differential equations. These estimates are based on local and global estimates for Fourier…

Analysis of PDEs · Mathematics 2021-02-24 Anders Israelsson , Salvador Rodriguez-Lopez , Wolfgang Staubach

We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and…

Numerical Analysis · Mathematics 2021-05-21 Costanza Conti , Sergio Lopez-Urena , Lucia Romani