Pseudo-differential operators have been developed as a tool for the study of elliptic differential equations. Suitably extended versions are also applicable to hypoelliptic equations, but their value is rather limited in genuinely non-elliptic problems. In this paper we shall therefore discuss some more general classes of operators which are adapted to such applications. For these operators we shall develop a calculus which is almost as smooth as that of pseudo-differential operators. It also seems that one gains some more insight into the theory of pseudo-differential operators by considering them from the point of view of the wider classes of operators to be discussed here so we shall take the opportunity to include a short exposition.

/pdf/fourier-integral-operators-i-1l7mhsqqcw.pdf

Fourier Integral Operators. I

L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

/pdf/elliptic-differential-operators-on-noncompact-manifolds-55ulflyd7e.pdf

Elliptic differential operators on noncompact manifolds

Analycity of the Semigroup Generated by the Stokes Operator.

Soit D un domaine borne de R n (n≥2) a frontiere lisse S, soit 1<r<∞ et soit X r la fermeture dans (L r (D)) n de tous les champs vectoriels solenoidaux lisses a support compact dans D. Soit W r m (D) l'espace de Sobolev d'ordre m et soit Δ le laplacien. On considere l'operateur de Stokes A r =−P r Δ de domaine D(A r )={w∈(W r 2 (D)) n ;w/5=0}MX 2 . Soit a un nombre reel positif. Pour chaque ∈ positif il y a une constante Ce a telle que ∥A r z ∥≤Ce a exp ∈|Im z | pour tout z satisfaisant −a<Rez<0, ou ∥A r z ∥ est la norme operateur de A r z

Domains of fractional powers of the Stokes operator in Lr spaces

Remarks on convergence of the Feynman path integrals

(1976). A caculus of fourier integral operators on Rn and the fundamental solution for an operator of hyperbolic type. Communications in Partial Differential Equations: Vol. 1, No. 1, pp. 1-44.

A caculus of fourier integral operators on Rn and the fundamental solution for an operator of hyperbolic type

/pdf/a-family-of-fourier-integral-operators-and-the-fundamental-kwnhr5oajp.pdf

A family of Fourier integral operators and the fundamental solution for a Schrödinger equation

(1978). Multi—products ofphase functions for fourier integral opertaors with an application. Communications in Partial Differential Equations: Vol. 3, No. 4, pp. 349-380.

Multi—products ofphase functions for fourier integral opertaors with an application

/pdf/complex-powers-of-hypoelliptic-pseudo-differential-operators-5a0diau3kw.pdf

Complex powers of hypoelliptic pseudo-differential operators with applications

/pdf/oscillatory-integrals-of-symbols-of-pseudo-differential-4q0vu4b999.pdf

Hitoshi Kumano-Go

Papers

A caculus of fourier integral operators on Rn and the fundamental solution for an operator of hyperbolic type

A family of Fourier integral operators and the fundamental solution for a Schrödinger equation

Multi—products ofphase functions for fourier integral opertaors with an application

Complex powers of hypoelliptic pseudo-differential operators with applications

Oscillatory Integrals of Symbols of Pseudo-Differential Operators on R n and Operators of Fredholm Type