Recent developments on Pseudo-Differential Operators (I)

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Published: Mar 30, 2015
DOI: https://doi.org/10.5556/j.tkjm.46.2015.1707
Keywords:
pseudo-differential operators boundary value problems operator-valued symbols Fourier transform

Main Article Content

D.-C. Chang
W. RUNGROTTHEERA
B.-W. SCHULZE

Abstract

In recent years the analysis of (pseudo-)differential operators on manifolds with second and higher order corners made considerable progress, and essential new structures have been developed. The main objective of this series of paper is to give a survey on the development of this theory in the past twenty years. We start with a brief background of the theory of pseudo-differential operators which including its symbolic calculus on $\R^n$. Next we introduce pseudo-differential calculus with operator-valued symbols. This allows us to discuss elliptic boundary value problems on smooth domains in $\R^n$ and elliptic problems on manifolds. This paper is based on the first part of lectures given by the authors while they visited the National Center for Theoretical Sciences in Hsinchu, Taiwan during May-July of 2014.

Article Details

How to Cite
Chang, D.-C., RUNGROTTHEERA, W., & SCHULZE, B.-W. (2015). Recent developments on Pseudo-Differential Operators (I). Tamkang Journal of Mathematics, 46(1), 1–30. https://doi.org/10.5556/j.tkjm.46.2015.1707
Issue
Vol. 46 No. 1 (2015)
Section
Survey Articles
Author Biographies

D.-C. Chang

Department of Mathematics and Department of Computer Science, Georgetown University, Washington D.C. 20057, USA.
Department ofMathematics, Fu Jen Catholic University, Taipei 242, Taiwan, ROC.

W. RUNGROTTHEERA

Department ofMathematics, Faculty of Science, Silpakorn University, Nakorn Pathom 73000, Thailand.

B.-W. SCHULZE

Institute ofMathematics, University of Potsdam, Am Neuen Palais 10, D-14469 Potsdam, Germany.

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