Fredholm Property of the Operator AR

1993 ◽  
pp. 188-204
Author(s):  
Bernhelm Booß-Bavnbek ◽  
Krzysztof P. Wojciechowski
Keyword(s):  
Fredholm Property

scholarly journals Existence of reaction-diffusion-convection waves in unbounded strips

2005 ◽  
Vol 2005 (2) ◽  
pp. 169-193 ◽  
Author(s):  
M. Belk ◽  
B. Kazmierczak ◽  
V. Volpert
Keyword(s):  
Implicit Function Theorem ◽  
Unbounded Domains ◽  
Reaction Diffusion ◽  
Fredholm Property ◽  
Implicit Function ◽  
Solvability Conditions ◽  
All Speeds ◽  
Diffusion Convection ◽  
Rayleigh Numbers ◽  
Property Index

Existence of reaction-diffusion-convection waves in unbounded strips is proved in the case of small Rayleigh numbers. In the bistable case the wave is unique, in the monostable case they exist for all speeds greater than the minimal one. The proof uses the implicit function theorem. Its application is based on the Fredholm property, index, and solvability conditions for elliptic problems in unbounded domains.

scholarly journals Wiener-Hopf equation and Fredholm property of the Goursat problem in Gevrey space

1994 ◽  
Vol 135 ◽  
pp. 165-196 ◽  
Author(s):  
Masatake Miyake ◽  
Masafumi Yoshino
Keyword(s):  
Differential Equations ◽  
Differential Operators ◽  
Newton Polygon ◽  
Index Theorem ◽  
Fredholm Property ◽  
Goursat Problem ◽  
Point Of View ◽  
Partial Differential ◽  
Partial Differential Operators ◽  
Gevrey Spaces

In the study of ordinary differential equations, Malgrange ([Ma]) and Ramis ([R1], [R2]) established index theorem in (formal) Gevrey spaces, and the notion of irregularity was nicely defined for the study of irregular points. In their studies, a Newton polygon has a great advantage to describe and understand the results in visual form. From this point of view, Miyake ([M2], [M3], [MH]) studied linear partial differential operators on (formal) Gevrey spaces and proved analogous results, and showed the validity of Newton polygon in the study of partial differential equations (see also [Yn]).

scholarly journals Elliptic operators and their symbols

2019 ◽  
Vol 52 (1) ◽  
pp. 361-369 ◽  
Author(s):  
Vladimir Vasilyev
Keyword(s):  
Fredholm Property ◽  
Elliptic Operators ◽  
Singular Points ◽  
Initial Operator

AbstractWe consider special elliptic operators in functional spaces on manifolds with a boundary which has some singular points. Such an operator can be represented by a sum of operators, and for a Fredholm property of an initial operator one needs a Fredholm property for each operator from this sum.

scholarly journals On the Fredholm Property of the Trace Operators Associated with the Elastic Layer Potentials

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 134 ◽  
Author(s):  
Giulio Starita ◽  
Alfonsina Tartaglione
Keyword(s):  
Elastic Body ◽  
Elastic Layer ◽  
Fredholm Property ◽  
System Of Equations ◽  
Layer Potentials ◽  
Connected Set ◽  
Equilibrium Configurations ◽  
Linear Elastostatics ◽  
Class C

We deal with the system of equations of linear elastostatics, governing the equilibrium configurations of a linearly elastic body. We recall the basics of the theory of the elastic layer potentials and we extend the trace operators associated with the layer potentials to suitable sets of singular densities. We prove that the trace operators defined, for example, on W 1 − k − 1 / q , q ( ∂ Ω ) (with k ≥ 2 , q ∈ ( 1 , + ∞ ) and Ω an open connected set of R 3 of class C k ), satisfy the Fredholm property.

scholarly journals A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Asao Arai
Keyword(s):  
Dirac Operator ◽  
Hilbert Spaces ◽  
Special Class ◽  
Spectral Properties ◽  
Fock Space ◽  
Dirac Operators ◽  
Fredholm Property ◽  
Perturbation Parameter ◽  
Coupling Constant ◽  
Infinite Dimensional

Spectral properties of a special class of infinite dimensional Dirac operatorsQ(α)on the abstract boson-fermion Fock spaceℱ(ℋ,𝒦)associated with the pair(ℋ,𝒦)of complex Hilbert spaces are investigated, whereα∈Cis a perturbation parameter (a coupling constant in the context of physics) and the unperturbed operatorQ(0)is taken to be a free infinite dimensional Dirac operator. A variety of the kernel ofQ(α)is shown. It is proved that there are cases where, for all sufficiently large|α|withα<0,Q(α)has infinitely many nonzero eigenvalues even ifQ(0)has no nonzero eigenvalues. Also Fredholm property ofQ(α)restricted to a subspace ofℱ(ℋ,𝒦)is discussed.

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