Fourier series with respect to general orthogonal systems
نویسندگان
چکیده
منابع مشابه
Fourier Series of Orthogonal Polynomials
It follows from Bateman [4] page 213 after setting = 1 2 . It can also be found with slight modi cation in Bateman [5] page122. However we are not aware of any reference where explicit formulas for the Fourier coef cients for Gegenbauer, Jacobi, Laguerre and Hermite polynomials can be found. In this article we use known formulas for the connection coef cients relating an arbitrary orthogonal po...
متن کاملSummation of Fourier Series with Respect to Walsh–like Systems and the Dyadic Derivative
In this paper we present some results on summability of oneand multi-dimensional Walsh-, Walsh-Kaczmarzand Vilenkin-Fourier series and on the dyadic and Vilenkin derivative. The Fejér and Cesàro summability methods are investigated. We will prove that the maximal operator of the summability means is bounded from the martingale Hardy space Hp to Lp (p > p0). For p = 1 we obtain a weak type inequ...
متن کاملSome Recent Results on Convergence and Divergence with Respect to Walsh-fourier Series
It is of main interest in the theory of Fourier series the reconstruction of a function from the partial sums of its Fourier series. Just to mention two examples: Billard proved [2] the theorem of Carleson for the Walsh-Paley system, that is, for each function in L we have the almost everywhere convergence Snf → f and Fine proved [4] the Fejér-Lebesgue theorem, that is for each integrable funct...
متن کاملSummability of Fourier Series with Respect to the Walsh–paley System
In the present paper we prove a number of statements dealing with the uniform convergence of Cesàro means of negative order of the Fourier– Walsh series. 1. Definitions and Notation Let r0(x) be the function defined by r0(x) = 1 if x ∈ [0, 12 ) , −1 if x ∈ 12 , 1 ) , r0(x+ 1) = r0(x). The Rademacher system is defined by rn(x) = r0(2x), n ≥ 1, and x ∈ [0, 1). Let ψ0(x), ψ1(x), ψ2(x), . . ....
متن کاملa comparison of teachers and supervisors, with respect to teacher efficacy and reflection
supervisors play an undeniable role in training teachers, before starting their professional experience by preparing them, at the initial years of their teaching by checking their work within the proper framework, and later on during their teaching by assessing their progress. but surprisingly, exploring their attributes, professional demands, and qualifications has remained a neglected theme i...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1976
ISSN: 0001-8708
DOI: 10.1016/0001-8708(76)90144-4