Harmonic Analysis pp 107-142 | Cite as
Conjugate Functions
Chapter
Abstract
The series conjugate to a trigonometric series
is
where sgn = 1 if n > 0, -1 if n < 0, and sg 0 = 0. Formally
such a series is oƒ analytic type.
$$
{\text{S = }}\sum\limits_{ - \infty }^\infty {{a_n}{e^{nix}}} $$
(1.1)
$$
T{\text{ = - }}i\sum\limits_{ - \infty }^\infty {({\text{sgn}}){a_n}{e^{nix}},} $$
(1.2)
$$
S + iT{\text{ = }}{{\text{a}}_0}{\text{ + 2}}\sum\limits_1^\infty {{a_n}{e^{nix}};} $$
(1.3)
Keywords
Fourier Series Positive Measure Trigonometric Polynomial Conjugate Function Trigonometric System
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
Copyright information
© Wadsworth, Inc., Belmont, California 1991