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Arithmetical Investigations: Representation Theory, Orthogonal Polynomials, and Quantum Interpolations - Couverture souple
Synopsis
In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
Présentation de l'éditeur
In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Arithmetical Investigations : Representation Theory, Orthogonal Polynomials, and Quantum Interpolations
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Arithmetical Investigations: Representation Theory, Orthogonal Polynomials, and Quantum Interpolations (Lecture Notes in Mathematics, 1941)
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Arithmetical Investigations (Paperback)
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Paperback. Etat : new. Paperback. In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums. In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9783540783787
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Arithmetical Investigations: Representation Theory, Orthogonal Polynomials, and Quantum Interpolations (Lecture Notes in Mathematics, 1941)
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Arithmetical Investigations
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Arithmetical Investigations : Representation Theory, Orthogonal Polynomials, and Quantum Interpolations
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Arithmetical Investigations
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Springer Berlin Heidelberg Mai 2008, 2008
ISBN 10 : 3540783784
ISBN 13 : 9783540783787
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on 'finite approximations' of [-1,1]. For special (gamma and beta) measures there is a 'quantum' or 'q-analogue' Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums. 236 pp. Englisch. N° de réf. du vendeur 9783540783787
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Arithmetical Investigations
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Arithmetical Investigations : Representation Theory, Orthogonal Polynomials, and Quantum Interpolations
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ISBN 10 : 3540783784
ISBN 13 : 9783540783787
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