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Integrals related to the Cantor function
Author(s):
E.
A.
Gorin;
B.
N.
Kukushkin
Translated by:
S. V. Kislyakov
Original publication:
Algebra i Analiz,
tom 15
(2003),
vypusk 3.
Journal:
St. Petersburg Math. J.
15
(2004),
449-468.
MSC (2000):
Primary 26A30
Posted:
March 31, 2004
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Additional information
References:
-
- 1.
- Victor H. Moll, The evaluation of integrals: a personal story, Notices Amer. Math. Soc. 49 (2002), no. 3, 311-317. MR 2002m:11105
- 2.
- A. Erdélyi, W. Magnus, F. Oberhettinger, and F. Tricomi, Higher transcendental functions. Vol. I, McGraw-Hill, New York, etc., 1953. MR 15:419i
- 3.
- E. Seneta, Regularly varying functions, Lecture Notes in Math., vol. 508, Springer-Verlag, Berlin-New York, 1976. MR 56:12189
- 4.
- N. M. Korobov, Trigonometric sums and their applications, ``Nauka'', Moscow, 1989; English transl., Exponential sums and their applications, Math. Appl. (Soviet Ser.), vol. 80, Kluwer Acad. Publishers Group, Dordrecht, 1992. MR 93a:11068
- 5.
- I. S. Gradshtein and I. M. Ryzhik, Table of integrals, sums, series, and products, 4th ed., Fizmatgiz, Moscow, 1962; English transl., Academic Press, New York-London, 1965. MR 28:5198
- 6.
- W. Rudin, Functional analysis, McGraw-Hill, New York, etc., 1973. MR 51:1315
- 7.
- E. C. Titchmarsh, The theory of the Riemann zeta-function, Clarendon Press, Oxford, 1951. MR 13:741c
- 8.
- B. Ya. Levin, Lectures on entire functions, Transl. Math. Monogr., vol. 150, Amer. Math. Soc., Providence, RI, 1996. MR 97j:30001
- 9.
- -, Distribution of zeros of entire functions, Gostekhizdat, Moscow, 1956; English transl., Amer. Math. Soc., Providence, RI, 1964. MR 28:217
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Additional Information:
E.
A.
Gorin
Affiliation:
Mathematics Department, Moscow State Pedagogical University, Moscow, Russia
Email:
evgeny.gorin@mtu-net.ru
B.
N.
Kukushkin
Affiliation:
Mathematics Department, Moscow State Pedagogical University, Moscow, Russia
DOI:
10.1090/S1061-0022-04-00817-9
PII:
S 1061-0022(04)00817-9
Keywords:
Cantor function,
Fourier transform,
Mellin transform
Received by editor(s):
10/JUN/2002
Posted:
March 31, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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