## 662 Citations

EXTENSION THEORY FOR ELLIPTIC PARTIAL DIFFERENTIAL OPERATORS WITH PSEUDODIFFERENTIAL METHODS

- Mathematics
- 2010

This is a short survey on the connection between general extension theories and the study of realizations of elliptic operators A on smooth domains in R n , n � 2. The theory of pseudodifferential…

Sharp estimates for a class of hyperbolic pseudo-differential equations

- Mathematics
- 2002

In this paper we consider the Cauchy problem for a class of hyperbolic pseudodifferential operators. The considered class contains constant coefficient differential equations, also allowing the…

Generalized Fourier Integral Operator Methods for Hyperbolic Equations with Singularities

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2013

Abstract This paper addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of…

On Carleman estimates for pseudo-differential operators

- Mathematics
- 1972

The original purpose of this work was to prove the regularity theorems in [1] without using Fourier integral operators. Instead we use the method of Carleman estimates of H6rmander ([3], Ch. 8), with…

Bilinear Fourier integral operators

- Mathematics
- 2010

We study the boundedness of bilinear Fourier integral operators on products of Lebesgue spaces. These operators are obtained from the class of bilinear pseudodifferential operators of Coifman and…

Geometric proofs of composition theorems for generalized Fourier integral operators.

- Mathematics
- 1999

The calculus of Fourier integral operators introduced by Hörmander in [11] has found widespread use throughout the study of linear partial differential equations. However, it is limited by the fact…

Pseudodifferential operators with generalized symbols and regularity theory

- Mathematics
- 2005

We study pseudodierential operators with amplitudes a"(x, ) depending on a singular parameter " ! 0 with asymptotic properties measured by dierent scales. We prove, taking into account the asymptotic…

A CLASS OF GENERALIZED INTEGRAL OPERATORS

- Mathematics
- 2009

In this paper, we introduce a class of generalized integral operators that includes Fourier integral operators. We establish some conditions on these operators such that they do not have bounded…

A note on a class of Fuchsian operators

- Mathematics
- 2013

We study the propagation of singularities of a class of higher order pseudo-differential operators with a real principal symbol and with a characteristic variety which is the union of two smooth…

Solution theory to Hyperbolic Stochastic Partial Differential Equations with polynomially bounded coefficients

- Mathematics
- 2016

We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. Both linear and semilinear equations are considered,under…