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001459972 001__ 1459972
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001459972 019__ $$a1370392123
001459972 020__ $$a9783031226847$$q(electronic bk.)
001459972 020__ $$a3031226844$$q(electronic bk.)
001459972 020__ $$z9783031226830
001459972 020__ $$z3031226836
001459972 0247_ $$a10.1007/978-3-031-22684-7$$2doi
001459972 035__ $$aSP(OCoLC)1370223385
001459972 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dEBLCP$$dUKAHL$$dYDX$$dSFB
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001459972 08204 $$a515/.732$$223/eng/20230216
001459972 1001_ $$aBan, Dubravka,$$eauthor.
001459972 24510 $$aP-adic banach space representations :$$bwith applications to principal series /$$cDubravka Ban.
001459972 264_1 $$aCham :$$bSpringer,$$c2023.
001459972 300__ $$a1 online resource (190 pages)
001459972 336__ $$atext$$btxt$$2rdacontent
001459972 337__ $$acomputer$$bc$$2rdamedia
001459972 338__ $$aonline resource$$bcr$$2rdacarrier
001459972 4901_ $$aLecture notes in mathematics ;$$vvolume 2325
001459972 5050_ $$aIntro -- Preface -- Contents -- 1 Introduction -- 1.1 Admissible Banach Space Representations -- 1.2 Principal Series Representations -- 1.3 Some Questions and Further Reading -- 1.4 Prerequisites -- 1.5 Notation -- 1.6 Groups -- Part I Banach Space Representations of p-adic Lie Groups -- 2 Iwasawa Algebras -- 2.1 Projective Limits -- 2.1.1 Universal Property of Projective Limits -- 2.1.2 Projective Limit Topology -- Cofinal Subsystem -- Morphisms of Inverse Systems -- 2.2 Projective Limits of Topological Groups and oK-Modules -- 2.2.1 Profinite Groups -- Topology on Profinite Groups
001459972 5058_ $$a2.3 Iwasawa Rings -- 2.3.1 Linear-Topological oK-Modules -- Definition of Iwasawa Algebra -- Fundamental System of Neighborhoods of Zero -- Embedding oK[G0], G0, and oK into oK[[G0]] -- 2.3.2 Another Projective Limit Realization of oK[[G0]] -- 2.3.3 Some Properties of Iwasawa Algebras -- Zero Divisors -- Augmentation Map -- Iwasawa Algebra of a Subgroup -- 3 Distributions -- 3.1 Locally Convex Vector Spaces -- 3.1.1 Banach Spaces -- 3.1.2 Continuous Linear Operators -- 3.1.3 Examples of Banach Spaces -- Banach Space of Bounded Functions -- Continuous Functions on G0 -- Mahler Expansion
001459972 5058_ $$a3.1.4 Double Duals of a Banach Space -- 3.2 Distributions -- 3.2.1 The Weak Topology on Dc(G0,oK) -- 3.2.2 Distributions and Iwasawa Rings -- 3.2.3 The Canonical Pairing -- 3.3 The Bounded-Weak Topology -- 3.3.1 The Bounded-Weak Topology is Strictly Finer than the Weak Topology -- The Weak Topology on V' -- The Bounded-Weak Topology on V' -- 3.4 Locally Convex Topology on K[[G0]] -- 3.4.1 The Canonical Pairing -- 3.4.2 p-adic Haar Measure -- 3.4.3 The Ring Structure on Dc(G0,K) -- A Big Projective Limit -- 4 Banach Space Representations -- 4.1 p-adic Lie Groups
001459972 5058_ $$a4.2 Linear Operators on Banach Spaces -- 4.2.1 Spherically Complete Spaces -- 4.2.2 Some Fundamental Theorems in Functional Analysis -- 4.2.3 Banach Space Representations: Definition and Basic Properties -- 4.3 Schneider-Teitelbaum Duality -- 4.3.1 Schikhof's Duality -- 4.3.2 Duality for Banach Space Representations: Iwasawa Modules -- K[[G0]]-module structure on V' -- 4.4 Admissible Banach Space Representations -- 4.4.1 Locally Analytic Vectors: Representations in Characteristic p -- Locally Analytic Vectors -- Unitary Representations and Reduction Modulo pK
001459972 5058_ $$a4.4.2 Duality for p-adic Lie Groups -- Part II Principal Series Representations of Reductive Groups -- Notation in Part II -- 5 Reductive Groups -- 5.1 Linear Algebraic Groups -- 5.1.1 Basic Properties of Linear Algebraic Groups -- More Examples of Linear Algebraic Groups -- Unipotent Subgroups -- Identity Component -- Tori -- 5.1.2 Lie Algebra of an Algebraic Group -- Lie Algebras -- Lie Algebra of an Algebraic Group -- 5.2 Reductive Groups Over Algebraically Closed Fields -- 5.2.1 Rational Characters -- 5.2.2 Roots of a Reductive Group -- Weyl Group -- Abstract Root Systems -- Simple Roots
001459972 506__ $$aAccess limited to authorized users.
001459972 520__ $$aThis book systematically develops the theory of continuous representations on p-adic Banach spaces. Its purpose is to lay the foundations of the representation theory of reductive p-adic groups on p-adic Banach spaces, explain the duality theory of Schneider and Teitelbaum, and demonstrate its applications to continuous principal series. Written to be accessible to graduate students, the book gives a comprehensive introduction to the necessary tools, including Iwasawa algebras, p-adic measures and distributions, p-adic functional analysis, reductive groups, and smooth and algebraic representations. Part 1 culminates with the duality between Banach space representations and Iwasawa modules. This duality is applied in Part 2 for studying the intertwining operators and reducibility of the continuous principal series on p-adic Banach spaces. This monograph is intended to serve both as a reference book and as an introductory text for graduate students and researchers entering the area.
001459972 588__ $$aDescription based on print version record.
001459972 650_0 $$aBanach spaces.
001459972 650_0 $$ap-adic analysis.
001459972 655_0 $$aElectronic books.
001459972 77608 $$iPrint version:$$aBan, Dubravka.$$tP-adic banach space representations.$$dCham : Springer Nature Switzerland, 2023$$z9783031226830$$w(OCoLC)1356959444
001459972 830_0 $$aLecture notes in mathematics (Springer-Verlag) ;$$vv. 2325.
001459972 852__ $$bebk
001459972 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-22684-7$$zOnline Access$$91397441.1
001459972 909CO $$ooai:library.usi.edu:1459972$$pGLOBAL_SET
001459972 980__ $$aBIB
001459972 980__ $$aEBOOK
001459972 982__ $$aEbook
001459972 983__ $$aOnline
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