1,721,078 research outputs found
Fourier integral operators algebra and fundamental solutions to hyperbolic systems with polynomially bounded coefficients on R^n
Full text linkWe study the composition of an arbitrary number of Fourier integral operators A(j), j = 1, ..., M, M >= 2, defined through symbols belonging to the so-called SG classes. We give conditions ensuring that the composition A(1) circle ... circle A(M) of such operators still belongs to the same class. Through this, we are then able to show well-posedness in weighted Sobolev spaces for first order hyperbolic systems of partial differential equations in SG classes, by constructing the associated fundamental solutions. These results expand the existing theory for the study of the properties "at infinity" of the solutions to hyperbolic Cauchy problems on R-n with polynomially bounded coefficients
Fourier integral operators and the index of symplectomorphisms on manifolds with boundary
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Solution theory to semilinear hyperbolic stochastic partial differential equations with polynomially bounded coefficients
Full text linkWe study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We provide conditions on the initial data and on the stochastic terms, namely, on the associated spectral measure, so that mild solutions exist and are unique in suitably chosen functional classes. More precisely, function-valued solutions are obtained, as well as a regularity result
Fourier type operators on Orlicz spaces and the role of Orlicz Lebesgue exponents
Full text linkWe deduce continuity properties of classes of Fourier multipliers,
pseudo-differential and Fourier integral operators when acting on Orlicz
spaces. Especially we show classical results like H{\"o}rmander's improvement
of Mihlin's Fourier multiplier theorem are extendable to the framework of
Orlicz spaces. We also show how some properties of the Young functions
of the Orlicz spaces are linked to properties of certain Lebesgue exponents
and emerged from
A Class of Fourier Integral Operators on Manifolds with Boundary
No full textWe study a class of Fourier integral operators on compact manifolds with boundary, associated with a natural class of symplectomorphisms, namely, those which preserve the boundary. A calculus of Boutet de Monvel's type can be defined for such Fourier integral operators, and appropriate continuity properties established. One of the key features of this calculus is that the local representations of these operators are given by operator-valued symbols acting on Schwartz functions or temperate distributions. Here we focus on properties of the corresponding local phase functions, which allow to prove this result in a rather straightforward wa
On Temperate Distributions Decaying at Infinity
No full textWe describe classes of temperate distributions with prescribed decay properties at infinity. The definition of the elements of such classes is given in terms of the Schwartz’ bounded distributions, and we discuss their characterization in terms of convolution and of decomposition as a finite sum of derivatives of suitable functions. We also prove mapping properties under the action of a class of Fourier integral operators, with inhomogeneous phase function and polynomially bounded symbol globally defined on R
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