منابع مشابه
Convergence of Fourier Series
The purpose of this paper is to explore the basic question of the convergence of Fourier series. This paper will not delve into the deeper questions of convergence that measure theory illuminates, but requires only the basic principles set out by introductory real and complex analysis.
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This paper will study Fourier Series with random coefficients. We begin with an introduction to Fourier series on the torus and give some of the most important results. We then give some important results from probability theory, and build on these to prove a variety of theorems that deal with the convergence or divergence of general random series. In the final section, the focus is placed on r...
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It is proved that the complex double Fourier series of an integrable function f (x,y) with coefficients {c jk} satisfying certain conditions, will converge in L 1norm. The conditions used here are the combinations of Tauberian condition of Hardy– Karamata kind and its limiting case. This paper extends the result of Bray [1] to complex double Fourier series.
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1955
ISSN: 0386-2194
DOI: 10.3792/pja/1195525770