Integrability of Multiple Trigonometric Series and Parseval′s Formula
نویسندگان
چکیده
منابع مشابه
Power-monotone Sequences and Integrability of Trigonometric Series
The theorem proved in this paper is a generalization of some results, concerning integrability of trigonometric series, due to R.P. Boas, L. Leindler, etc. This result can be considered as an example showing the utility of the notion of power-monotone sequences.
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In 1870 Cantor proved that representation of a function of one variable by a trigonometric series can be done in only one way. In 1996 Bourgain proved the same thing for spherical convergence and multiple trigonometric series. His proof involves injecting a lot of new ideas into the theory of uniqueness. We give here an exposition of Bourgain’s proof, specialized to the case of dimension 2. Our...
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Abstract. The paper is related to the following question of P. L. Ul’yanov: is it true that for any 2π-periodic continuous function f there is a uniformly convergent rearrangement of its trigonometric Fourier series? In particular, we give an affirmative answer if the absolute values of Fourier coefficients of f decrease. Also, we study a problem how to choose m terms of a trigonometric polynom...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1994
ISSN: 0022-247X
DOI: 10.1006/jmaa.1994.1293