This article investigates a function f(x), constructed from the Nikol’skii class in S2. The estimation obtained will show that the Riesz mean of the spectral expansions is unable to be strengthened due to absence of localization caused by a singualrity at a definite point f(x), on the sphere.
REFERENCES
1.
2.
A. K.
Pulatov
, Mathematical Notes of the Academy of Sciences of the USSR
22
, 517
–523
(1977
).3.
V. V.
Khocholava
, Bulletin of the Academy of Sciences of the Georgian SSR
93
, 33
–36
(1979
).4.
T. H.
Gronwall
, Math. Ann.
75
, 321
–375
(1914
).5.
6.
A. K.
Pulatov
, Mathematical Notes of the Academy of Sciences of the USSR
14
, 1076
–1080
(1978
).7.
8.
9.
10.
A. A.
Rakhimov
, “Localization of spectral expansions,” in International training-seminars on mathematics
(2011
).11.
A. A.
Rakhimov
, “On the uniform convergence of the eigenfunction expansions,” in Journal of Physics: Conference Series
, Vol. 435
(IOP Publishing
, UK
, 2013
) p. 012010
.12.
A. A.
Ahmedov
, Journal of Mathematical Analysis and Applications
56
, 310
–321
(2009
).13.
A. A.
Ahmedov
, A. F. N.
Rasedee
, and A. A.
Rakhimov
, Malaysian Journal of Mathematical Sciences
7
, 315
–326
(2013
).14.
A. A.
Ahmedov
and A. F. N.
Rasedee
, Malaysian Journal of Mathematical Sciences
9
, 337
–348
(2015
).15.
A. F. N.
Rasedee
, “Spectral expansions of Laplace-Beltrami operator on unit sphere
,” Ph.D. thesis, University Putra of Malaysia
, Selangor, Malaysia
2015
.
This content is only available via PDF.
© 2017 Author(s).
2017
Author(s)
You do not currently have access to this content.