Hendrik de Snoo's Books

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

By: Daniel Alpay,Aad Dijksma,James Rovnyak,Hendrik de Snoo

Write a review Read reviews Take a Quiz Solve Book Puzzle

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

By: Daniel Alpay,Aad Dijksma,James Rovnyak,Hendrik de Snoo

Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

244

Publisher

Birkhäuser

Published Date

ISBN 10

3034889089

ISBN 13

9783034889087

Effective Results and Methods for Diophantine Equations over Finitely Generated Domains

By: Jan-Hendrik Evertse,Kálmán Győry

Write a review Read reviews Take a Quiz Solve Book Puzzle

Effective Results and Methods for Diophantine Equations over Finitely Generated Domains

By: Jan-Hendrik Evertse,Kálmán Győry

This book provides the first thorough treatment of effective results and methods for Diophantine equations over finitely generated domains. Compiling diverse results and techniques from papers written in recent decades, the text includes an in-depth analysis of classical equations including unit equations, Thue equations, hyper- and superelliptic equations, the Catalan equation, discriminant equations and decomposable form equations. The majority of results are proved in a quantitative form, giving effective bounds on the sizes of the solutions. The necessary techniques from Diophantine approximation and commutative algebra are all explained in detail without requiring any specialized knowledge on the topic, enabling readers from beginning graduate students to experts to prove effective finiteness results for various further classes of Diophantine equations.

Average ratings

N/A