{"product_id":"a-primer-on-the-dirichlet-space-hardback-9781107047525","title":"A Primer on the Dirichlet Space (Hardback) 9781107047525","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eA Primer on the Dirichlet Space\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThe first systematic account of the Dirichlet space, one of the most fundamental Hilbert spaces of analytic functions.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eOmar El-Fallah (Author), Karim Kellay (Author), Javad Mashreghi (Author), Thomas Ransford (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781107047525, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 16 January 2014\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e226 pages, 5 b\/w illus.  110 exercises\u003cbr\u003e23.1 x 15.2 x 2.3 cm, 0.47 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e 1. Basic notions\u003cbr\u003e 2. Capacity\u003cbr\u003e 3. Boundary behavior\u003cbr\u003e 4. Zero sets\u003cbr\u003e 5. Multipliers\u003cbr\u003e 6. Conformal invariance\u003cbr\u003e 7. Harmonically weighted Dirichlet spaces\u003cbr\u003e 8. Invariant subspaces\u003cbr\u003e 9. Cyclicity\u003cbr\u003e Appendix A. Hardy spaces\u003cbr\u003e Appendix B. The Hardy–Littlewood maximal function\u003cbr\u003e Appendix C. Positive definite matrices\u003cbr\u003e Appendix D. Regularization and the rising-sun lemma\u003cbr\u003e References\u003cbr\u003e Index of notation\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Functional analysis \u0026amp; transforms [\u003ca title=\"See our other books on Functional analysis \u0026amp; transforms\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Functional%20analysis%20\u0026amp;%20transforms%20%5BPBKF%5D%22\"\u003ePBKF\u003c\/a\u003e], Complex analysis, complex variables [\u003ca title=\"See our other books on Complex analysis, complex variables\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Complex%20analysis,%20complex%20variables%20%5BPBKD%5D%22\"\u003ePBKD\u003c\/a\u003e], Real analysis, real variables [\u003ca title=\"See our other books on Real analysis, real variables\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Real%20analysis,%20real%20variables%20%5BPBKB%5D%22\"\u003ePBKB\u003c\/a\u003e], Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46004888895768,"sku":"9781107047525","price":68.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781107047525i_1d02d529-61f2-47e3-a0ae-8932a29e6423.jpg?v=1691361605","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/a-primer-on-the-dirichlet-space-hardback-9781107047525","provider":"Freshly Printed Books","version":"1.0","type":"link"}