António Ferreira dos Santos

Operator Theoretical Methods and Applications to Mathematical Physics

Preface.- Part A: Honoring Erhard Meister. Introduction. Obituary. C.V. Publications. PhD Students. Reminiscences and Miscellanea.- Part B: Papers on Operator Theoretical Methods and Applications to Mathematical Physics.

Generalized factorization for a class of 2 × 2 matrix functions with non-rational entries

The problems of existence and calculation of a generalized factorization for a class of non-rational matrix functions are examined. The class considered, which consist of 2 × 2 matrix functions whose elements are of form , has not, up to now, been studied and existing methods of factorization do not apply to it. Such matrix functions may appear e.g. in relation to boundary-value problems involving fourth order differential operators (α =1/4). The authors derive necessary and sufficient conditions for the existence of a canonical factorization and give explicit formulas for the factors.

The Lisbon Connection

We recall, with emotion, our first meeting with Erhard Meister, in August 1988, in Calgary, during the IWOTA conference to commemorate the 60th anniversary of Israel Gohberg. Erhard Meister had a charming personality, something which made a strong impact on our group. His invitation for further contacts was promptly accepted by us and led to a long-lasting cooperation between the Darmstadt and the Lisbon groups.

Publications of Erhard Meister

1. Randwertaufgaben der Funktionentheorie. Mit Anwendungen auf singulare Integralgleichungen und Schwingungsprobleme der mathematischen Physik.— Leitfaden der Angewandten Mathematik und Mechanik, Vol. 59, B.G. Teubner, Stuttgart 1983, 320 pp.