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Books on the topic 'Jacobi polynomials'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 January 2023

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1

Askey, R. A. Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Providence, R.I., U.S.A: American Mathematical Society, 1985.

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2

1951-, Wilson James Arthur, ed. Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Providence, R.I., U.S.A: American Mathematical Society, 1985.

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3

Kalnins, E. G. Orthogonal polynomials on N-spheres: Gegenbauer, Jacobi, and Heun. Hamilton, N.Z: University of Waikato, 1990.

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4

Transplantation theorems and multiplier theorems for Jacobi series. Providence, R.I: American Mathematical Society, 1986.

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5

Muckenhoupt, Benjamin. Transplantation theorems and multiplier theorems for Jacobi series. Providence, R.I., USA: American Mathematical Society, 1986.

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6

Forrester, Peter. Log-gases and random matrices. Princeton: Princeton University Press, 2010.

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7

Log-gases and random matrices. Princeton: Princeton University Press, 2010.

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8

Chanillo, Sagun. Weak type estimates for Cesaro sums of Jacobi polynomial series. Providence, R.I: American Mathematical Society, 1993.

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9

van den Essen, Arno, Shigeru Kuroda, and Anthony J. Crachiola. Polynomial Automorphisms and the Jacobian Conjecture. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-60535-3.

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10

Yau, Stephen S. T. Classification of Jacobian ideals in variant by sl (2, c) actions. Providence, R.I., USA: American Mathematical Society, 1988.

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11

Yau, Stephen Shing-Toung. Classification of Jacobian ideals invariant by sl(2, C) actions. Providence, R.I., USA: American Mathematical Society, 1988.

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12

Dyson, Freeman. Spectral statistics of unitary ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.4.

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This article focuses on the use of the orthogonal polynomial method for computing correlation functions, cluster functions, gap probability, Janossy density, and spacing distributions for the eigenvalues of matrix ensembles with unitary-invariant probability law. It first considers the classical families of orthogonal polynomials (Hermite, Laguerre, and Jacobi) and some corresponding unitary ensembles before discussing the statistical properties of N-tuples of real numbers. It then reviews the definitions of basic statistical quantities and demonstrates how their distributions can be made explicit in terms of orthogonal polynomials. It also describes the k-point correlation function, Fredholm determinants of finite-rank kernels, and resolvent kernels.

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13

Anderson, Greg W. Spectral statistics of orthogonal and symplectic ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.5.

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This article describes a direct approach for computing scalar and matrix kernels, respectively for the unitary ensembles on the one hand and the orthogonal and symplectic ensembles on the other hand, leading to correlation functions and gap probabilities. In the classical orthogonal polynomials (Hermite, Laguerre, and Jacobi), the matrix kernels for the orthogonal and symplectic ensemble are expressed in terms of the scalar kernel for the unitary case, using the relation between the classical orthogonal polynomials going with the unitary ensembles and the skew-orthogonal polynomials going with the orthogonal and symplectic ensembles. The article states the fundamental theorem relating the orthonormal and skew-orthonormal polynomials that enter into the Christoffel-Darboux kernels

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14

Polynomial Automorphisms and the Jacobian Conjecture. Birkhauser, 2000.

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15

Essen, Arno van den. Polynomial Automorphisms: And the Jacobian Conjecture. Birkhauser Verlag, 2012.

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16

Essen, Arno van den. Polynomial Automorphisms: And the Jacobian Conjecture (Progress in Mathematics). Birkhäuser Basel, 2000.

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17

Crachiola, Anthony J., Arno van den Essen, and Shigeru Kuroda. Polynomial Automorphisms and the Jacobian Conjecture: New Results from the Beginning of the 21st Century. Springer International Publishing AG, 2021.

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18

Tanasa, Adrian. Combinatorial Physics. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895493.001.0001.

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After briefly presenting (for the physicist) some notions frequently used in combinatorics (such as graphs or combinatorial maps) and after briefly presenting (for the combinatorialist) the main concepts of quantum field theory (QFT), the book shows how algebraic combinatorics can be used to deal with perturbative renormalisation (both in commutative and non-commutative quantum field theory), how analytic combinatorics can be used for QFT issues (again, for both commutative and non-commutative QFT), how Grassmann integrals (frequently used in QFT) can be used to proCve new combinatorial identities (generalizing the Lindström–Gessel–Viennot formula), how combinatorial QFT can bring a new insight on the celebrated Jacobian conjecture (which concerns global invertibility of polynomial systems) and so on. In the second part of the book, matrix models, and tensor models are presented to the reader as QFT models. Several tensor model results (such as the implementation of the large N limit and of the double-scaling limit for various such tensor models, N being here the size of the tensor) are then exposed. These results are natural generalizations of results extensively used by theoretical physicists in the study of matrix models and they are obtained through intensive use of combinatorial techniques (this time mainly enumerative techniques). The last part of the book is dedicated to the recently discovered relation between tensor models and the holographic Sachdev–Ye–Kitaev model, model which has been extensively studied in the last years by condensed matter and by high-energy physicists.

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