1,721,045 research outputs found
Pseudodifferential operators and spaces of type S
No full textWe study a class of pseudodifferential operators in in the frame of the spaces of type S of Gelfand and Shilov
Gelfand spaces and pseudodifferential operators of infinite order in R^n
No full textThe aim of this work is to study a class of symbols of infinite order and to develop a global calculus for the corresponding pseudodifferential operators. In particular, we obtain results of boundedness for the operators and of global regularity for the solutions of the associated equations in the Gelfand spaces
Pseudodifferential parametrices of infinite order and SG-hyperbolic problems
No full textIn this paper we consider a class of symbols of infinite order and develop a global calculus for the related pseudodifferential operators in the functional frame of the Gelfand-Shilov spaces of type S. As an application, we construct a parametrix for the Cauchy problem associated to an operator with principal part and lower order terms given by SG-operators, cf. Introduction. We do not assume here Levi conditions on the lower order terms. Giving initial data in Gelfand-Shilov spaces, we are able to prove the well-posedness for the problem and to give an explicit expression of the solution
Wave front set at infinity for tempered ultradistributions and hyperbolic equations
No full textWe study the propagation of singularities and the microlocal behaviour at infinity for the solution of the Cauchy problem associated to an SG-hyperbolic operator with one characteristic of constant multiplicity.
We perform our analysis in the framework of tempered ultradistributions, cf. Introduction, using an appropriate notion of wave front set
Fourier Integral Operators and Gelfand-Shilov Spaces
No full textIn this work, we study a class of Fourier integral operators of infinite
order acting on the Gelfand-Shilov spaces of type S. We also define wave front sets in terms of Gelfand-Shilov classes and study the action of the
previous Fourier integral operators on them
Fourier integral operators of infinite order and applications to SG-hyperbolic equations
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Pointwise decay and smoothness for semilinear elliptic equations and travelling waves
Full text linkWe derive sharp decay estimates and prove holomorphic extensions for the solutions of a class of semilinear nonlocal elliptic equations with linear part given by a sum of Fourier multipliers with finitely smooth symbols at the origin. Applications concern the decay and smoothness of travelling waves for nonlinear evolution equations in fluid dynamics and plasma physics
SG-pseudodifferential operators and Gelfand-Shilov spaces
No full textIn this paper, we study a class of pseudo-differential operators of SG type in the functional setting of the Gelfand-Shilov spaces . As an application we prove a result of hypoellipticity in the same classes. In the last of the paper, we define a notion of wave front set for tempered ultradistributions which allows to describe both the local regularity and the behaviour at infinity of the elements of the dual space
THE CAUCHY PROBLEM FOR QUASILINEAR SG-HYPERBOLIC SYSTEMS
No full textWe study the Cauchy problem for a class of quasilinear hyperbolic systems with coefficients depending on (t, x) \in [0, T ] \times R^n and presenting a linear growth for |x | tending to + infinity. We prove well-posedness in the Schwartz space S(R^n). The result is obtained by deriving an energy estimate for the solution of the linearized problem in some weighted Sobolev spaces and applying a fixed point argument
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