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nonlinear fourier transform terence tao, christoph thiele [pdf]

The Nonlinear Fourier Transform by Terence Tao, Christoph Thiele, Ya-Ju Tsai

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About this book :-
The Nonlinear Fourier Transform written by Terence Tao
cover the topics nonlinear fourier, dirac scattering and SU(2) scattering transform.

Book Detail :-
Title: The Nonlinear Fourier Transform
Author(s): Terence Tao, Christoph Thiele, Ya-Ju Tsai
Year: 1991
Pages: 196
Type: PDF
Language: English
Country: US
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About Author :-
Author Terence Tao is an Australian mathematician. He was born on 1975 in South Australia. His father was a Chinese paediatricain.
He is a professor of mathematics at the University of California, Los Angeles. His area of research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing, analytic number theory and representation theory. He was awarded the Fields Medal in 2006 and MacArthur Fellowship awarded in 2007.

All Famous Books of this Author :-
Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.
• Download PDF An Epsilon of Room, I: Real Analysis by Terence Tao NEW
• Download PDF An Introduction to Measure Theory by Terence Tao NEW
• Download PDF The Nonlinear Fourier Transform by Terence Tao NEW

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Book Contents :-
The Nonlinear Fourier Transform written by Terence Tao cover the following topics.
1. The nonlinear Fourier transform
Introduction, The nonlinear Fourier transform on l0, l, The nonlinear Fourier transform, The image of finite sequences, Extension to l1, sequences, Extension to lp sequences, 1 < p < 2, The nonlinear Fourier transform on l2(Z=0), Extension to half-infinite l2, sequences, Higher order variants of the Plancherel identity, The nonlinear Fourier transform on l2, (Z), The forward NLFT on l2(Z), Existence and uniqueness of an inverse NLFT for bounded a , Existence of an inverse NLFT for unbounded a, Rational functions as Fourier transform data, The Riemann-Hilbert problem for rational functions, Orthogonal polynomials, Orthogonal polynomials on T and the nonlinear Fourier transform, Jacobi matrices and the nonlinear Fourier transform, Further applications, Integrable systems, Gaussian processes, Appendix: Some Background material, The boundary behaviour of holomorphic functions, The group Sl2(R) and friends
2. The Dirac scattering transform
Introduction, Functions on the circle, disk, and exterior disk, Matrix-valued functions on the disk, The non-linear Fourier transform for compactly supported potentials, The non-linear Fourier transform on half-line potentials, The NLFT on the whole line Z, Connection between the NLFT and the Lax operator L, Scattering theory, A flag of Hilbert spaces, Proof of triple factorization, Lax pair
3. The SU(2) scattering transform
Introduction, SU(2) NLFT on Finite Sequences and (Z, C), Extension to half line, sequences, Rational Functions as Fourier Transform Data, Soliton Data, Bibliography


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