{"product_id":"9781032922218-course-in-abstract-harmonic-analysis","title":"A Course in Abstract Harmonic Analysis","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003eThis book presents the essentials of harmonic analysis on locally compact groups in a concise and accessible form. The text provides necessary background on Banach algebras and spectral theory, develops the theory of analysis on Abelian groups and compact groups, examines the theory of induced representations, and explores the theory of represen\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eA Course in Abstract Harmonic Analysis\u003c\/strong\u003e is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant results and techniques that are of interest in their own right. \u003c\/p\u003e\n\u003cp\u003eThis book develops the abstract theory along with a well-chosen selection of concrete examples that exemplify the results and show the breadth of their applicability. After a preliminary chapter containing the necessary background material on Banach algebras and spectral theory, the text sets out the general theory of locally compact groups and their unitary representations, followed by a development of the more specific theory of analysis on Abelian groups and compact groups. There is an extensive chapter on the theory of induced representations and its applications, and the book concludes with a more informal exposition on the theory of representations of non-Abelian, non-compact groups.\u003c\/p\u003e\n\u003cp\u003eFeaturing extensive updates and new examples, the \u003cb\u003eSecond Edition\u003c\/b\u003e:\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eAdds a short section on von Neumann algebras\u003c\/li\u003e\n\u003cli\u003eIncludes Mark Kac’s simple proof of a restricted form of Wiener’s theorem\u003c\/li\u003e\n\u003cli\u003eExplains the relation between \u003ci\u003eSU\u003c\/i\u003e(2) and \u003ci\u003eSO\u003c\/i\u003e(3) in terms of quaternions, an elegant method that brings \u003ci\u003eSO\u003c\/i\u003e(4) into the picture with little effort\u003c\/li\u003e\n\u003cli\u003eDiscusses representations of the discrete Heisenberg group and its central quotients, illustrating the Mackey machine for regular semi-direct products and the pathological phenomena for nonregular ones\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cb\u003eA Course in Abstract Harmonic Analysis, Second Edition \u003c\/b\u003eserves as an entrée to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form.\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":56434717884790,"sku":"9781032922218","price":67.85,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/stand_36623773.jpg?v=1760563129","url":"https:\/\/www.rarewaves.com\/products\/9781032922218-course-in-abstract-harmonic-analysis","provider":"Rarewaves.com","version":"1.0","type":"link"}