Behrndt / Gohberg / Förster Spectral Theory in Inner Product Spaces and Applications

6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, Berlin, December 2006
2009
ISBN: 978-3-7643-8911-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 188, 250 Seiten, eBook

Reihe: Operator Theory: Advances and Applications

This book contains a collection of recent research papers originating from the 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, which was held at the TU Berlin, Germany, December 14 to 17, 2006. The contributions in this volume are devoted to spectral and perturbation theory of linear operators in spaces with an inner product, generalized Nevanlinna functions and problems and applications in the field of differential equations. Among the discussed topics are linear relations, singular perturbations, de Branges spaces, nonnegative matrices and abstract kinetic equations.

Zielgruppe

Research

Autoren/Hrsg.

Gohberg, I

Alpay, D

Arazy, J

Atzmon, A

Bart, H

Ben-Artzi, A

Bercovici, H

Böttcher, A

Cla, K

Behrndt, Jussi

Förster, Karl-Heinz

Langer, Heinz

Trunk, Carsten

Inhaltsverzeichnis

Augmented Schur Parameters for Generalized Nevanlinna Functions and Approximation.- On Domains of Powers of Linear Operators and Finite Rank Perturbations.- Finite-dimensional de Branges Subspaces Generated by Majorants.- Trace Formulae for Dissipative and Coupled Scattering Systems.- Approximation of N ? ? -functions I: Models and Regularization.- On the Block Numerical Range of Nonnegative Matrices.- A Quantum Dot with Impurity in the Lobachevsky Plane.- One-dimensional Perturbations, Asymptotic Expansions, and Spectral Gaps.- Abstract Kinetic Equations with Positive Collision Operators.- On the Structure of Semigroups of Operators Acting in Spaces with Indefinite Metric.- G-Self-adjoint Operators in Almost Pontryagin Spaces.- On a Kre?n Criterion.- Two-sided Weighted Shifts Are ‘Almost Krein’ Normal.

Leseproben

After Dinner Speech on the Inventor of the Equality Sign (S. XIII-XIV)

Aad Dijksma

The day after tomorrow I will have the pleasure of having attended all four Berlin workshops on Operator Theory in Krein spaces. At the ?rst workshop there were four speakers: Tomas Azizov, Hagen Neidhardt, Yuri Shondin, and myself. Since then the number of speakers has increased steadily to 41. Moreover, the number of days has increased.

The ?rst workshop was held for one day in November, now it is spread out over three days in December. What has not changed is that each speaker is allotted the same amount of time for his or her lecture: one hour each at the ?rst workshop and 25 minutes each now. Indeed, it is a characteristic and nice feature of these Berlin workshops that we are all treated equally. For this reason I would like to say a few words about equality, or more precisely about the equality sign. Although this may seem a sudden digression to you, for me it is not as I will explain.

This summer I attended workshops in Newcastle and Cardi?, and Myra, my wife, accompanied me. After Cardi? we spent a week camping in South Wales along the coast near Tenby, now a tourist center with a very picturesque colorful harbor. Centuries ago it was a major port. One day we were hiking along the Pembroke coast when we met an English couple. We started talking and when I told them that I was a mathematician they said, “Oh, but then you are in the right place, because the inventor of the equality sign is born right here in Tenby. There is a commemorative plaque in St Mary’s Church.”

The next day we went to the church and found the shield on a pillar honoring Robert Recorde as the inventor of the equality sign. He was born in Tenby in 1510, almost 500 years ago. I do not know how it is with you, but before this event I had never really much thought about who invented which sign and was a bit sceptical. But that changed after I spoke with my colleague at the University of Groningen Jan van Maanen, who is a specialist in the History of Mathematics. He knew the name of Robert Recorde quite well and to learn more about such inventions he recommended Florian Cajori’s A history of mathematical notations published in two large volumes in 1928–29, now available as a Dover pocket edition [1].

Anyway, I became interested in this Robert Recorde. The following information is taken from the website [2] of the St. Andrews University on the History of Mathematics. Robert Recorde studied medicine ?rst in Cambridge and then in Oxford. He was highly educated and taught in both places. In 1545 he moved to London where he became the court physician to King Edward VI and Queen Mary. In 1549 he was appointed as the controller of the Bristol mint and later he was placed in charge of the silver mines in Wexford, Ireland and was made the technical supervisor of the Dublin mint.

In this capacity he introduced the silver crown of ?ve shillings which was the ?rst English coin to have a date written in Arabic numerals rather than in Roman numerals. Robert Recorde was not always very tactical in his dealings with the intrigues of the court and sometimes lost favour. In 1556 he tried to charge his arch-enemey at court, the Earl of Pembroke, with misconduct in order to regain his position. Recorde may have had a valid case, but the Earl would not allow a minor servant like Recorde to get the better of him. He countered Recorde’s charges by suing him for libel.