Fourier Analysis and ApproximationFourier Analysis and Approximation |
Contents
| 25 | |
Fourier Transforms | 163 |
Hilbert Transforms | 303 |
Characterization of Certain Function Classes | 355 |
Saturation Theory | 431 |
List of Symbols | 511 |
Tables of Fourier and Hilbert Transforms | 515 |
| 521 | |
| 547 | |
| 554 | |
Other editions - View all
Fourier Analysis and Approximation, Volume 1; Volume 40 Paul Leo Butzer,Rolf Joachim Nessel No preview available - 1971 |
Common terms and phrases
6-factor apply approximate identity assertions are equivalent Banach space bounded linear characterizations conjugate constant continuous function convergence convolution defined definition denotes Dºf dominated convergence theorem Dººf du(u exists g e f belongs Favard class fe Län fe Lip fe WIL fe X(R fe X2 Fejér's type finite Fourier transform formula Fourier series Fourier–Stieltjes transform Fubini's theorem function f Furthermore given Hence Hilbert transform Hint Hölder's inequality Iffe implies inversion isgn kernel x,(x Lemma limn Lºn Moreover norm order of approximation particular Peano derivative periodic functions pointwise positive Problem Proposition prove representation Riemann derivative rth Peano satisfies saturation sequence singular integral singular integral I,(f ſº solution strong Riesz derivative tends to zero theory trigonometric trigonometric polynomial u e BV uniformly Weierstrass