{"product_id":"integration-and-harmonic-analysis-on-compact-groups-paperback-9780521097178","title":"Integration and Harmonic Analysis on Compact Groups (Paperback \/ softback) 9780521097178","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eIntegration and Harmonic Analysis on Compact Groups\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThese notes provide a reasonably self-contained introductory survey of certain aspects of harmonic analysis on compact groups.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eR. E. Edwards (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521097178, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 7 September 1972\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e192 pages\u003cbr\u003e22.9 x 15.2 x 1.1 cm, 0.29 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\"\u003eThese notes provide a reasonably self-contained introductory survey of certain aspects of harmonic analysis on compact groups. The first part of the book seeks to give a brief account of integration theory on compact Hausdorff spaces. The second, larger part starts from the existence and essential uniqueness of an invariant integral on every compact Hausdorff group. Topics subsequently outlined include representations, the Peter–Weyl theory, positive definite functions, summability and convergence, spans of translates, closed ideals and invariant subspaces, spectral synthesis problems, the Hausdorff-Young theorem, and lacunarity.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eGeneral Introduction\u003cbr\u003e Acknowledgements\u003cbr\u003e Part I. Integration and the Riesz representation theorem: 1. Preliminaries regarding measures and integrals\u003cbr\u003e 2. Statement and discussion of Riesz's theorem\u003cbr\u003e 3. Method of proof of RRT: preliminaries\u003cbr\u003e 4. First stage of extension of I\u003cbr\u003e 5. Second stage of extension of I\u003cbr\u003e 6. The space of integrable functions\u003cbr\u003e 7. The a- measure associated with I: proof of the RRT\u003cbr\u003e 8. Lebesgue's convergence theorem\u003cbr\u003e 9. Concerning the necessity of the hypotheses in the RRT\u003cbr\u003e 10. Historical remarks\u003cbr\u003e 11. Complex-valued functions\u003cbr\u003e Part II. Harmonic analysis on compact groups\u003cbr\u003e 12. Invariant integration\u003cbr\u003e 13. Group representations\u003cbr\u003e 14. The Fourier transform\u003cbr\u003e 15. The completeness and uniqueness theorems\u003cbr\u003e 16. Schur's lemma and its consequences\u003cbr\u003e 17. The orthogonality relations\u003cbr\u003e 18. Fourier series in L2(G)\u003cbr\u003e 19. Positive definite functions\u003cbr\u003e 20. Summability and convergence of Fourier series\u003cbr\u003e 21. Closed spans of translates\u003cbr\u003e 22. Structural building bricks and spectra\u003cbr\u003e 23. Closed ideals and closed invariant subspaces\u003cbr\u003e 24. Spectral synthesis problems\u003cbr\u003e 25. The Hausdorff-Young theorem\u003cbr\u003e 26. Lacunarity.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: 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":46006386589976,"sku":"9780521097178","price":54.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521097178i_cb335a3b-96d8-4a8f-801f-c5a6ccd48bed.jpg?v=1694970614","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/integration-and-harmonic-analysis-on-compact-groups-paperback-9780521097178","provider":"Freshly Printed Books","version":"1.0","type":"link"}