On L1 convergence of Fourier series of complex valued functions
نویسندگان
چکیده
منابع مشابه
On L Convergence of Fourier Series of Complex Valued Functions
In the present paper, we give a brief review of L 1-convergence of trigonometric series. Previous known results in this direction are improved and generalized by establishing a new condition.
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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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Let D be a non empty set and let E be a complex-membered set. One can verify that every element of D→̇E is complex-valued. Let D be a non empty set, let E be a complex-membered set, and let F1, F2 be elements of D→̇E. Then F1 + F2 is an element of D→̇C. Then F1 − F2 is an element of D→̇C. Then F1 · F2 is an element of D→̇C. Then F1/F2 is an element of D→̇C. Let D be a non empty set, let E be a comple...
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ژورنال
عنوان ژورنال: Studia Scientiarum Mathematicarum Hungarica
سال: 2007
ISSN: 0081-6906,1588-2896
DOI: 10.1556/sscmath.2006.1004