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Nonlinear Fourier Transform by Terence Tao, Christoph Thiele
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About this book :-
Nonlinear Fourier Transform written by
Terence Tao, Christoph Thiele.
Book Detail :-
Title: Nonlinear Fourier Transform
Edition:
Author(s): Terence Tao, Christoph Thiele
Publisher:
Series:
Year:
Pages: 196
Type: PDF
Language: English
ISBN:
Country:
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Book Contents :-
Nonlinear Fourier Transform written by
Terence Tao, Christoph Thiele
cover the following topics.
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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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