Affiliation:
1. Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK
2. Department of Mathematics, School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
Abstract
The basis and regularity properties of the generalized trigonometric functions
sin
p
,
q
and
cos
p
,
q
are investigated. Upper bounds for the Fourier coefficients of these functions are given. Conditions are obtained under which the functions
cos
p
,
q
generate a basis of every Lebesgue space
L
r
(0,1) with
1
<
r
<
∞
; when
q
is the conjugate of
p
, it is sufficient to require that
p
∈[
p
1
,
p
2
], where
p
1
<2 and
p
2
>2 are calculable numbers. A comparison is made of the speed of decay of the Fourier sine coefficients of a function in Lebesgue and Lorentz sequence spaces with that of the corresponding coefficients with respect to the functions
sin
p
,
q
.
These results sharpen previously known ones.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Reference15 articles.
1. Elbert Á. 1981 A half-linear second order differential equation. In Qualitative theory of differential equations vol. I II (Szeged 1979). Colloq. Math. Soc. János Bolyai vol. 30 pp. 153–180. Amsterdam The Netherlands/New York NY: North-Holland.
2. A remark on certain nonlinear elliptic equations;Ôtani M;Proc. Fac. Sci. Tokai Univ.,1984
3. Lindqvist P. 1993 Some remarkable sine and cosine functions. Helsingin Teknillinen Korkeakoulu. Matematiikan Laitos.
4. Basis properties of eigenfunctions of the 𝑝-Laplacian
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