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1. |
Record Nr. |
UNINA9910480947803321 |
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Autore |
Brown Ron <1943-> |
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Titolo |
Frobenius groups and classical maximal orders / / Ron Brown |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 2001 |
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ISBN |
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Descrizione fisica |
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1 online resource (125 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 717 |
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Disciplina |
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Soggetti |
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Frobenius groups |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"Volume 151, number 717 (third of 5 numbers)." |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Lemmas on Truncated Group Rings""; ""Chapter 3. Groups of Real Quaternions""; ""Chapter 4. Proof of the Classification Theorem""; ""Chapter 5. Frobenius complements with core index 1""; ""Chapter 6. Frobenius complements with core index 4""; ""Chapter 7. Frobenius complements with core index 12""; ""Chapter 8. Frobenius complements with core index 24""; ""Chapter 9. Frobenius complements with core index 60""; ""Chapter 10. Frobenius complements with core index 120""; ""Chapter 11. Counting Frobenius Complements"" |
""Chapter 12. Maximal Orders""""Chapter 13. Isomorphism Classes of Frobenius Groups with Abelian Frobenius Kernel""; ""Chapter 14. Concrete Constructions of Frobenius Groups""; ""Chapter 15. Counting Frobenius Groups with Abelian Frobenius Kernel""; ""Chapter 16. Isomorphism Invariants for Frobenius Complements""; ""Chapter 17. Schur Indices and Finite Subgroups of Division Rings""; ""Bibliography"" |
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2. |
Record Nr. |
UNINA9910798386803321 |
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Autore |
Ikromov Isroil A. <1961-> |
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Titolo |
Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra / / Isroil A. Ikromov and Detlef Müller |
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Pubbl/distr/stampa |
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Princeton : , : Princeton University Press, , [2016] |
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ISBN |
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Descrizione fisica |
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1 online resource (269 p.) |
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Collana |
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Annals of mathematics studies ; ; number 194 |
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Classificazione |
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Disciplina |
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Soggetti |
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Hypersurfaces |
Polyhedra |
Surfaces, Algebraic |
Fourier analysis |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Frontmatter -- Contents -- Chapter 1. Introduction -- Chapter 2. Auxiliary Results -- Chapter 3. Reduction to Restriction Estimates near the Principal Root Jet -- Chapter 4. Restriction for Surfaces with Linear Height below 2 -- Chapter 5. Improved Estimates by Means of Airy-Type Analysis -- Chapter 6. The Case When hlin(Φ) ≥ 2: Preparatory Results -- Chapter 7. How to Go beyond the Case hlin(Φ) ≥ 5 -- Chapter 8. The Remaining Cases Where m = 2 and B = 3 or B = 4 -- Chapter 9. Proofs of Propositions 1.7 and 1.17 -- Bibliography -- Index |
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Sommario/riassunto |
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This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces. The range of Lebesgue spaces for which these estimates are valid is described in terms of Newton polyhedra associated to the given surface.Isroil Ikromov and Detlef Müller begin with Elias M. Stein's concept of Fourier restriction and some relations between the decay of the Fourier transform of the surface measure and Stein-Tomas type restriction estimates. Varchenko's ideas relating Fourier decay to associated Newton polyhedra are briefly explained, particularly the concept of adapted coordinates and the notion of height. It turns out |
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that these classical tools essentially suffice already to treat the case where there exist linear adapted coordinates, and thus Ikromov and Müller concentrate on the remaining case. Here the notion of r-height is introduced, which proves to be the right new concept. They then describe decomposition techniques and related stopping time algorithms that allow to partition the given surface into various pieces, which can eventually be handled by means of oscillatory integral estimates. Different interpolation techniques are presented and used, from complex to more recent real methods by Bak and Seeger.Fourier restriction plays an important role in several fields, in particular in real and harmonic analysis, number theory, and PDEs. This book will interest graduate students and researchers working in such fields. |
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