A Primer on the Dirichlet Space
eBook - PDF

A Primer on the Dirichlet Space

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

A Primer on the Dirichlet Space

About this book

The Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles, and improving upon many of the proofs. Topics treated include: the Douglas and Carleson formulas for the Dirichlet integral, reproducing kernels, boundary behaviour and capacity, zero sets and uniqueness sets, multipliers, interpolation, Carleson measures, composition operators, local Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special features include a self-contained treatment of capacity, including the strong-type inequality. The book will be valuable to researchers in function theory, and with over 100 exercises it is also suitable for self-study by graduate students.

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Yes, you can access A Primer on the Dirichlet Space by Omar El-Fallah,Karim Kellay,Javad Mashreghi,Thomas Ransford in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half Title
  3. Series Page
  4. Title Page
  5. Imprints
  6. Dedication
  7. Contents
  8. Preface
  9. 1 Basic notions
  10. 2 Capacity
  11. 3 Boundary behavior
  12. 4 Zero sets
  13. 5 Multipliers
  14. 6 Conformal invariance
  15. 7 Harmonically weighted Dirichlet spaces
  16. 8 Invariant subspaces
  17. 9 Cyclicity
  18. Appendix A Hardy spaces
  19. Appendix B The Hardy–Littlewood maximal function
  20. Appendix C Positive definite matrices
  21. Appendix D Regularization and the rising-sun lemma
  22. References
  23. Index of notation
  24. Index