Results 301 to 310 of about 282,183 (352)

Fourier Integral Operators

1994
The theory of pseudo differential operators, discussed in § 1, is well suited for investigating various problems connected with elliptic differential equations. However, this theory fails to be adequate for studying equations of hyperbolic type, and one is then forced to examine a wider class of operators, the so-called Fourier integral operators ...
Yu. V. Egorov, M. A. Shubin
openaire   +1 more source

A Class of Fourier Integral Operators on Manifolds with Boundary

, 2014
We study a class of Fourier integral operators on compact manifolds with boundary X and Y , associated with a natural class of symplectomorphisms \(\mathcal{X} :\;T^{*}Y \; \backslash \;0\rightarrow\;T^{*}X\; \backslash \;0\), namely, those which ...
U. Battisti, S. Coriasco, E. Schrohe
semanticscholar   +1 more source

Fourier Integral Operators in SG Classes: Classical Operators

2001
We continue the investigation of the calculus of Fourier Integral Operators (FIOs) in the class of symbols with exit behaviour (SG symbols). Here we analyse what happens when one restricts the choice of amplitude and phase functions to the subclass of the classical SG symbols.
CORIASCO, Sandro, P. PANARESE
openaire   +2 more sources

Neural Operators with Localized Integral and Differential Kernels

International Conference on Machine Learning
Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications.
Miguel Liu-Schiaffini, Julius Berner, B. Bonev, Thorsten Kurth, K. Azizzadenesheli, Anima Anandkumar   +5 more
semanticscholar   +1 more source

Fourier integral operators with cusp singularities

American Journal of Mathematics, 1998
We study the boundedness properties, on Lebesgue and Sobolev spaces, of Fourier integral operators associated with canonical relations such that at least one of the projections is a simple (Whitney) cusp. In the process, we obtain decay estimates for oscillatory integral operators whose symplectic relations have the same singular structure.
Greenleaf, Allan, Seeger, Andreas
openaire   +1 more source

Regularity of Fourier Integral Operators

1995
The purpose of this paper is to survey some developments in the study of Radon transforms. These operators and the related oscillatory integrals have long been of interest in harmonic analysis and mathematical physics. Lately, they have emerged as key analytic tools in a wide variety of problems, ranging from partial differential equations to ...
openaire   +1 more source

Fourier Integral Operators and Gelfand-Shilov Spaces

2005
In 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.
openaire   +3 more sources

Remarks on Fourier Integral Operators

2004
We prove some estimates on several types of Fourier integral operators, emphasizing ɧ1→ ɧ1 estimates and ɧ→ bmo estimates. The results are mostly special cases of more general known results, but the proofs of the special cases presented here are simpler than the usual proofs. Furthermore, the special cases treated here arise quite commonly.
openaire   +1 more source

Feynman path integral regularization using Fourier Integral Operator ζ-functions

, 2018
T. Hartung
semanticscholar   +1 more source

A multi-FPGA application-specific architecture for accelerating a floating point Fourier Integral Operator

2008 International Conference on Application-Specific Systems, Architectures and Processors, 2008
Jason Lee, Lesley Shannon, M. Yedlin, G. Margrave   +3 more
semanticscholar   +1 more source