scholarly journals Comparison Tauberian theorems and hyperbolic operators with constant coefficients

2015 ◽  
Vol 7 (3) ◽  
pp. 47-53 ◽  
Author(s):  
Yurii Nikolaevich Drozhzhinov ◽  
Boris Ivanovich Zavialov
Keyword(s):  
Tauberian Theorems ◽  
Hyperbolic Operators ◽  
Constant Coefficients

Hyperbolic Convolution Operators

1965 ◽  
Vol 17 ◽  
pp. 559-582
Author(s):  
Takao Kakita
Keyword(s):  
Fundamental Solution ◽  
Compact Support ◽  
Differential Operators ◽  
Cone Condition ◽  
Convolution Operators ◽  
Hyperbolic Operators ◽  
Constant Coefficients

Hyperbolic differential operators with constant coefficients introduced and studied systematically by Gårding (4), were characterized by the existence of the fundamental solution with some cone condition, according to Hörmander (6). Recently Ehrenpreis, extending the notion of hyperbolicity due to Gårding, has defined hyperbolic operators for distributions with compact support in the convolution sense. Under the hypothesis that the operator is invertible as a distribution, he has established a theorem analogous to the theorem of Hörmander mentioned above (3).

scholarly journals Inhomogeneous Gevrey ultradistributions and Cauchy problem

2006 ◽  
Vol 133 (31) ◽  
pp. 176-186
Author(s):  
Daniela Calvo ◽  
L. Rodino
Keyword(s):  
Cauchy Problem ◽  
Weight Function ◽  
Differential Operators ◽  
Subject Classification ◽  
Well Posedness ◽  
Gevrey Classes ◽  
Partial Differential Operators ◽  
Hyperbolic Operators ◽  
The Cauchy Problem ◽  
Constant Coefficients

After a short survey on Gevrey functions and ultradistributions, we present the inhomogeneous Gevrey ultradistributions introduced recently by the authors in collaboration with A. Morando, cf. [7]. Their definition depends on a given weight function ?, satisfying suitable hypotheses, according to Liess-Rodino [16]. As an application, we define (s, ?)-hyperbolic partial differential operators with constant coefficients (for s > 1), and prove for them the well-posedness of the Cauchy problem in the frame of the corresponding inhomogeneous ultradistributions. This sets in the dual spaces a similar result of Calvo [4] in the inhomogeneous Gevrey classes, that in turn extends a previous result of Larsson [14] for weakly hyperbolic operators in standard homogeneous Gevrey classes. AMS Mathematics Subject Classification (2000): 46F05, 35E15, 35S05.

Differential p-forms and q-vector fields with constant coefficients

2020 ◽  
pp. 1
Author(s):  
Jaime Muñoz Masqué ◽  
Luis M. Pozo Coronado ◽  
M. Eugenia Rosado
Keyword(s):  
Vector Fields ◽  
Constant Coefficients ◽  
Q Vector

Classical Tauberian Theorems for the (C; 1; 1) Summability Method

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Ümit Totur
Keyword(s):  
Tauberian Theorem ◽  
Summability Method ◽  
Subject Classification ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Littlewood Theorem

Abstract In this paper we generalize some classical Tauberian theorems for single sequences to double sequences. One-sided Tauberian theorem and generalized Littlewood theorem for (C; 1; 1) summability method are given as corollaries of the main results. Mathematics Subject Classification 2010: 40E05, 40G0

scholarly journals Coarse cohomology with twisted coefficients

2020 ◽  
Vol 70 (6) ◽  
pp. 1413-1444
Author(s):  
Elisa Hartmann
Keyword(s):  
Sheaf Cohomology ◽  
Grothendieck Topology ◽  
Coarse Structure ◽  
Relative Cohomology ◽  
Number Of Ends ◽  
Constant Coefficients ◽  
Coarse Space ◽  
Grothendieck Topologies

AbstractTo a coarse structure we associate a Grothendieck topology which is determined by coarse covers. A coarse map between coarse spaces gives rise to a morphism of Grothendieck topologies. This way we define sheaves and sheaf cohomology on coarse spaces. We obtain that sheaf cohomology is a functor on the coarse category: if two coarse maps are close they induce the same map in cohomology. There is a coarse version of a Mayer-Vietoris sequence and for every inclusion of coarse spaces there is a coarse version of relative cohomology. Cohomology with constant coefficients can be computed using the number of ends of a coarse space.

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