The Order of Magnitude of the Fourier Coefficients in Functions Having Isolated Singularities

1955 ◽  
Vol 62 (3) ◽  
pp. 149
Author(s):  
Gordon Raisbeck
Keyword(s):  
Fourier Coefficients ◽  
Isolated Singularities ◽  
Order Of Magnitude

Order of magnitude of multiple Fourier coefficients of functions of bounded p-variation

2010 ◽  
Vol 128 (4) ◽  
pp. 328-343 ◽  
Author(s):  
B. L. Ghodadra
Keyword(s):  
Fourier Coefficients ◽  
Order Of Magnitude

Order of magnitude of multiple fourier coefficients of functions of bounded variation

2004 ◽  
Vol 104 (1/2) ◽  
pp. 95-104 ◽  
Author(s):  
Vanda Fülöp ◽  
Ferenc Móricz
Keyword(s):  
Bounded Variation ◽  
Fourier Coefficients ◽  
Functions Of Bounded Variation ◽  
Order Of Magnitude

On the Order of Magnitude of the Fourier Coefficients of a Function Integrable in C λ L Sense

1946 ◽  
Vol s1-21 (3) ◽  
pp. 198-203 ◽  
Author(s):  
W. L. C. Sargent
Keyword(s):  
Fourier Coefficients ◽  
Order Of Magnitude

Fourier coefficients of cusp forms

1986 ◽  
Vol 100 (1) ◽  
pp. 5-29 ◽  
Author(s):  
R. A. Rankin
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Cusp Forms ◽  
Modular Functions ◽  
Field Of Study ◽  
Important Paper ◽  
Present Survey ◽  
Arithmetical Functions ◽  
Survey Article ◽  
Order Of Magnitude

The object of this survey article is to trace the influence on the theory of modular forms of the ideas contained in L. J. Mordell's important paper ‘On Mr Ramanujan's empirical expansions of modular functions’, which appeared in October 1917 in this Society's Proceedings [32]. The equally important paper [42] by S. Ramanujan, ‘On certain arithmetical functions’, referred to in Mordell's title, was published in May 1916 in the same Society's older journal, the Transactions, which was regrettably suppressed in 1928, 107 years after its foundation. Ramanujan's paper was concerned not only with multiplicative properties of Fourier coefficients of modular forms, but also with their order of magnitude. Since subsequent papers on the latter subject have also appeared in the Proceedings, it seems appropriate to include further developments in this field of study in the present survey.

On the Order of Magnitude of Fourier Coefficients with Hadamard's Gaps

1962 ◽  
Vol s1-37 (1) ◽  
pp. 117-120
Author(s):  
M. Tomić
Keyword(s):  
Fourier Coefficients ◽  
Order Of Magnitude

scholarly journals Absolutely convergent Fourier series and generalized Zygmund classes of functions

2009 ◽  
Vol 104 (1) ◽  
pp. 124
Author(s):  
Ferenc Móricz
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Fourier Coefficients ◽  
Sufficient Conditions ◽  
Modulus Of Smoothness ◽  
Slowly Varying Function ◽  
Continuous Periodic Function ◽  
Convergent Fourier Series ◽  
Period 2 ◽  
Order Of Magnitude

We investigate the order of magnitude of the modulus of smoothness of a function $f$ with absolutely convergent Fourier series. We give sufficient conditions in terms of the Fourier coefficients in order that $f$ belongs to one of the generalized Zygmund classes $(\mathrm{Zyg}(\alpha, L)$ and $(\mathrm{Zyg} (\alpha, 1/L)$, where $0\le \alpha\le 2$ and $L= L(x)$ is a positive, nondecreasing, slowly varying function and such that $L(x) \to \infty$ as $x\to \infty$. A continuous periodic function $f$ with period $2\pi$ is said to belong to the class $(\mathrm{Zyg} (\alpha, L)$ if 26740 |f(x+h) - 2f(x) + f(x-h)| \le C h^\alpha L\left(\frac{1}{h}\right)\qquad \text{for all $x\in \mathsf T$ and $h>0$}, 26740 where the constant $C$ does not depend on $x$ and $h$; and the class $(\mathrm{Zyg} (\alpha, 1/L)$ is defined analogously. The above sufficient conditions are also necessary in case the Fourier coefficients of $f$ are all nonnegative.

On the order of magnitude of Haar-Fourier coefficients

2009 ◽  
Vol 35 (4) ◽  
pp. 301-316 ◽  
Author(s):  
V. Sh. Tsagereishvili
Keyword(s):  
Fourier Coefficients ◽  
Order Of Magnitude
Sign in / Sign up

Export Citation Format

Share Document