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Books on the topic 'Frobenius's theorem'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Nussbaum, Roger D. Generalizations of the Perron-Frobenius theorem for nonlinear maps. Providence, R.I: American Mathematical Society, 1999.

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2

Peter, Sarnak, ed. Random matrices, Frobenius eigenvalues, and monodromy. Providence, R.I: American Mathematical Society, 1999.

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3

Society, London Mathematical, ed. Frobenius algebras and 2D topological quantum field theories. Cambridge: Cambridge University Press, 2003.

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4

1944-, Nussbaum Roger D., ed. Nonlinear Perron-Frobenius theory. Cambridge: Cambridge University Press, 2012.

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5

Josef, Leydold, and Stadler Peter F. 1965-, eds. Laplacian eigenvectors of graphs: Perron-Frobenius and Faber-Krahn type theorems. Berlin: Springer, 2007.

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6

I, Manin I͡U. Frobenius manifolds, quantum cohomology, and moduli spaces. Providence, RI: American Mathematical Society, 1999.

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7

Frobenius manifolds and moduli spaces for singularities. Cambridge: Cambridge University Press, 2002.

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8

Popov, A. M. Gruppy s sistemami frobeniusovykh podgrupp: Monografii︠a︡. Krasnoi︠a︡rsk: Krasnoi︠a︡rskiĭ gos. tekhnicheskiĭ universitet, 2004.

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9

Shparlinski, Igor E., and David R. Kohel. Frobenius distributions: Lang-Trotter and Sato-Tate conjectures : Winter School on Frobenius Distributions on Curves, February 17-21, 2014 [and] Workshop on Frobenius Distributions on Curves, February 24-28, 2014, Centre International de Rencontres Mathematiques, Marseille, France. Providence, Rhode Island: American Mathematical Society, 2016.

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10

Patrick, Solé, ed. Codes over rings: Proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008. Singapore: World Scientific, 2009.

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11

1966-, Jarvis Tyler Jamison, Kimura Takashi 1963-, and Vaintrob Arkady 1956-, eds. Gromov-Witten theory of spin curves and orbifolds: AMS Special Session on Gromov-Witten Theory of Spin Curves and Orbifolds, May 3-4, 2003, San Francisco State University, San Francisco, California. Providence, R.I: American Mathematical Society, 2006.

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12

Session, Ring Theory. Ring theory and its applications: Ring Theory Session in honor of T.Y. Lam on his 70th birthday at the 31st Ohio State-Denison Mathematics Conference, May 25-27, 2012, The Ohio State University, Columbus, OH. Edited by Lam, T. Y. (Tsit-Yuen), 1942- honouree, Huynh, Dinh Van, 1947- editor of compilation, and Ohio State-Denison Mathematics Conference. Providence, Rhode Island: American Mathematical Society, 2014.

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13

Polcino, Milies César, ed. Groups, algebras and applications: XVIII Latin American Algebra Colloquium, August 3-8, 2009, São Pedro, SP, Brazil. Providence, R.I: American Mathematical Society, 2011.

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14

Conference on Hopf Algebras and Tensor Categories (2011 University of Almeria). Hopf algebras and tensor categories: International conference, July 4-8, 2011, University of Almería, Almería, Spain. Edited by Andruskiewitsch Nicolás 1958-, Cuadra Juan 1975-, and Torrecillas B. (Blas) 1958-. Providence, Rhode Island: American Mathematical Society, 2013.

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15

(Dietmar), Salamon D., ed. J-holomorphic curves and symplectic topology. 2nd ed. Providence, R.I: American Mathematical Society, 2012.

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16

Street, Brian. Multi-parameter Singular Integrals. (AM-189). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691162515.001.0001.

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This book develops a new theory of multi-parameter singular integrals associated with Carnot–Carathéodory balls. The book first details the classical theory of Calderón–Zygmund singular integrals and applications to linear partial differential equations. It then outlines the theory of multi-parameter Carnot–Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. The book then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples. This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. This book will interest graduate students and researchers working in singular integrals and related fields.

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17

Street, Brian. The Calder´on-Zygmund Theory II: Maximal Hypoellipticity. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691162515.003.0002.

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This chapter remains in the single-parameter case and turns to the case when the metric is a Carnot–Carathéodory (or sub-Riemannian) metric. It defines a class of singular integral operators adapted to this metric. The chapter has two major themes. The first is a more general reprise of the trichotomy described in Chapter 1 (Theorem 2.0.29). The second theme is a generalization of the fact that Euclidean singular integral operators are closely related to elliptic partial differential equations. The chapter also introduces a quantitative version of the classical Frobenius theorem from differential geometry. This “quantitative Frobenius theorem” can be thought of as yielding “scaling maps” which are well adapted to the Carnot–Carathéodory geometry, and is of central use throughout the rest of the monograph.

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18

Kock, Joachim. Frobenius Algebras and 2-D Topological Quantum Field Theories (London Mathematical Society Student Texts). Cambridge University Press, 2004.

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19

Kock, Joachim. Frobenius Algebras and 2-D Topological Quantum Field Theories (London Mathematical Society Student Texts). Cambridge University Press, 2004.

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20

Street, Brian. Multi-parameter Carnot-Carath´eodory Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691162515.003.0003.

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This chapter develops the theory of multi-parameter Carnot–Carathéodory geometry, which is needed to study singular integral operators. In the case when the balls are of product type, all of the results are simple variants of results in the single-parameter theory. When the balls are not of product type, these ideas become more difficult. What saves the day is the quantitative Frobenius theorem given in Chapter 2. This can be used to estimate certain integrals, as well as develop an appropriate maximal function and an appropriate Littlewood–Paley square function, all of which are essential to our study of singular integral operators.

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21

Leydold, Josef, Peter F. Stadler, and Türker Biyikoglu. Laplacian Eigenvectors of Graphs: Perron-Frobenius and Faber-Krahn Type Theorems (Lecture Notes in Mathematics Book 1915). Springer, 2007.

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22

Heunen, Chris, and Jamie Vicary. Categories for Quantum Theory. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198739623.001.0001.

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Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition and a conceptual way to understand many high-level quantum phenomena. Here, we lay the foundations for this categorical quantum mechanics, with an emphasis on the graphical calculus that makes computation intuitive. We describe superposition and entanglement using biproducts and dual objects, and show how quantum teleportation can be studied abstractly using these structures. We investigate monoids, Frobenius structures and Hopf algebras, showing how they can be used to model classical information and complementary observables. We describe the CP construction, a categorical tool to describe probabilistic quantum systems. The last chapter introduces higher categories, surface diagrams and 2-Hilbert spaces, and shows how the language of duality in monoidal 2-categories can be used to reason about quantum protocols, including quantum teleportation and dense coding. Previous knowledge of linear algebra, quantum information or category theory would give an ideal background for studying this text, but it is not assumed, with essential background material given in a self-contained introductory chapter. Throughout the text, we point out links with many other areas, such as representation theory, topology, quantum algebra, knot theory and probability theory, and present nonstandard models including sets and relations. All results are stated rigorously and full proofs are given as far as possible, making this book an invaluable reference for modern techniques in quantum logic, with much of the material not available in any other textbook.

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