Harmonic Analysis on Classical Groups

Sheng Gong (Autor)

Buch | Softcover

XII, 265 Seiten

2012 | Softcover reprint of the original 1st ed. 1991
Springer Berlin (Verlag)
978-3-642-63498-7 (ISBN)

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H.Weyl studied harmonic analysis on compact groups of finite di mension. He proved that an orthonormal system exists and that any continuous function on these groups can be approximated by some tinite linear combination of functions in this system. His research, however, seems to be too abstract to yield an explicit expression for the orthonormal system. Thus, we cannot talk about the form of the approximation, nor about its convergence. iO The simplest example of compact groups is {e }, on which there exists an orthonormal system inO { e }, n = 0, ± 1, ± 2 , ... , namely 1 J2" ." ." {I, for n = m; - e,n"e-1m"dO = 2n 0 0, for n =;6 m. The harmonic analysis on this compact group refers to the whole Fourier analysis. So far, extensive literature has been available on this topic. Its remarkable progress is evidenced by the great monograph of seven-hundred pages in two volumes written by A. Zygmund in 1959. iO An immediate extension for {e } is group U", which consists of all n X n square matrices U satisfying ufj' = I, where fj' denotes the conjugate transpose matrix of U. As for construction, there is a close relation between the group U and the group S03. Besides, 2 the application of U" has been found more and more important in physics.

I. Harmonic Analysis on Unitary Groups.- 0. Preliminary.- 1. Abel Summation of Fourier Series on Unitary Groups.- 2. Cesàro Summations of Fourier Series on Unitary Groups.- 3. Partial Sum of Fourier Series on Unitary Groups.- 4. On Peter-Weyl Theorem.- 5. Spherical Summation of Fourier Series on Unitary Groups.- II. Harmonic Analysis on Rotation Groups.- 6. Abel Summation of Fourier Series on Rotation Groups.- 7. Cesàro Summation of Fourier Series on Rotation Groups.- 8. Partial Sum of Fourier Series on Rotation Groups.- 9. Spherical Summation of Fourier Series on Rotation Groups.- III. Harmonic Analysis on Unitary Symplectic Groups.- 10. The Volume of Unitary Symplectic Group and Criteria of Convergence of Fourier Series.- 11. Cesàro and Abel Summation of Fourier Series on Unitary Symplectic Groups.- 12. Spherical Summation of Fourier Series on Unitary Symplectic Groups.- 13. Harmonic Analysis in Classical Domains on Quaternion Field.- Epilogue.- References.

Erscheint lt. Verlag	10.11.2012
Zusatzinfo	XII, 265 p.
Verlagsort	Berlin
Sprache	englisch
Maße	170 x 242 mm
Gewicht	487 g
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Fourier-Reihe • Fourier series • Harmonic Analysis • Harmonische Analyse • Poisson-Formel • Poisson Formula • Rotation Groups • Rotationsgruppe • Unitäre Gruppen • Unitary Groups
ISBN-10	3-642-63498-2 / 3642634982
ISBN-13	978-3-642-63498-7 / 9783642634987
Zustand	Neuware