Calculus for Fourier Integral Operators in generalized SG classes

Abstract

We construct a calculus for generalized $\mathbf{SG}$ Fourier integral operators, extending known results to a broader class of symbols of $\mathbf{SG}$ type. In particular, we do not require that the phase functions are homogeneous. We also prove the $L^2({\mathbf{R}}^d)$-boundedness of the generalized $\mathbf{SG}$ Fourier integral operators having regular phase functions and amplitudes uniformly bounded on ${\mathbf{R}}^{2d}$.

42 pages. arXiv admin note: substantial text overlap with arXiv:1307.6249

Cited by in corpus (1)

• Fourier integral operators algebra and fundamental solutions to hyperbolic systems with polynomially bounded coefficients on R^n