scholarly journals Noncoercive differential operators on homogeneous manifolds of negative curvature and their Green functions

2001 ◽  
Vol 88 (1) ◽  
pp. 121-134
Author(s):  
Roman Urban
Keyword(s):  
Negative Curvature ◽  
Differential Operators ◽  
Green Functions ◽  
Homogeneous Manifolds

scholarly journals Boundary Value Problems with Integral Gluing Conditions for Fractional-Order Mixed-Type Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
A. S. Berdyshev ◽  
E. T. Karimov ◽  
N. Akhtaeva
Keyword(s):  
Mixed Type ◽  
Differential Operators ◽  
Type Equation ◽  
Telegraph Equation ◽  
Fractional Diffusion ◽  
Tricomi Problem ◽  
Green Functions ◽  
Mixed Type Equation ◽  
Energy Integrals ◽  
Gellerstedt Problem

Analogs of the Tricomi and the Gellerstedt problems with integral gluing conditions for mixed parabolic-hyperbolic equation with parameter have been considered. The considered mixed-type equation consists of fractional diffusion and telegraph equation. The Tricomi problem is equivalently reduced to the second-kind Volterra integral equation, which is uniquely solvable. The uniqueness of the Gellerstedt problem is proven by energy integrals' method and the existence by reducing it to the ordinary differential equations. The method of Green functions and properties of integral-differential operators have been used.

scholarly journals On the nuclear trace of Fourier integral operators

2019 ◽  
Vol 37 (2) ◽  
pp. 219-249
Author(s):  
Duván Cardona
Keyword(s):  
Symmetric Spaces ◽  
Differential Operators ◽  
Integral Operators ◽  
Fourier Integral ◽  
Fourier Integral Operators ◽  
Weyl Quantization ◽  
Homogeneous Manifolds ◽  
Dimensional Torus ◽  
Lebesgue Spaces ◽  
Pseudo Differential Operators

In this paper we characterise ther-nuclearity of Fourier integraloperators on Lebesgue spaces. Fourier integral operators will be consideredinRn,the discrete groupZn,then-dimensional torus and symmetric spaces(compact homogeneous manifolds). We also give formulae forthe nucleartrace of these operators. Explicit examples will be given onZn,the torusTn,the special unitary group SU(2),and the projective complex planeCP2.Ourmain theorems will be applied to the characterization ofr-nuclear pseudo-differential operators defined by the Weyl quantization procedure.

Homogeneous manifolds with negative curvature. II

1976 ◽  
Vol 8 (178) ◽  
pp. 0-0 ◽  
Author(s):  
Robert Azencott ◽  
Edward N. Wilson
Keyword(s):  
Negative Curvature ◽  
Homogeneous Manifolds
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