This systematic account of the Dirichlet space provides an introduction that will be valuable to researchers in function theory, assembling results previously only found in scattered research articles. Containing more than 100 exercises, the book is also suitable for self-study by graduate students in mathematics.
This systematic account of the Dirichlet space provides an introduction that will be valuable to researchers in function theory, assembling results previously only found in scattered research articles. Containing more than 100 exercises, the book is also suitable for self-study by graduate students in mathematics.
Omar El-Fallah is professor at Université Mohammed V-Agdal in Rabat, Morocco. He has published more than twenty research articles and has supervised eight doctoral students.
Inhaltsangabe
Preface 1. Basic notions 2. Capacity 3. Boundary behavior 4. Zero sets 5. Multipliers 6. Conformal invariance 7. Harmonically weighted Dirichlet spaces 8. Invariant subspaces 9. Cyclicity Appendix A. Hardy spaces Appendix B. The Hardy-Littlewood maximal function Appendix C. Positive definite matrices Appendix D. Regularization and the rising-sun lemma References Index of notation Index.
Preface 1. Basic notions 2. Capacity 3. Boundary behavior 4. Zero sets 5. Multipliers 6. Conformal invariance 7. Harmonically weighted Dirichlet spaces 8. Invariant subspaces 9. Cyclicity Appendix A. Hardy spaces Appendix B. The Hardy-Littlewood maximal function Appendix C. Positive definite matrices Appendix D. Regularization and the rising-sun lemma References Index of notation Index.
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