martingale convergence theoremThe paper deals with convergence of the Fourier series of q-Besicovitch almost periodic functions of the form $$ f(t)sim mathop{sum}limits_{m=1}^{infty }{a_m}{{mathrm{e}}^{{-mathrm{i}{uplambda_m}t}}}, $$where {λm} is a Dirichlet sequence, that ...
4.3.5 Convergence of the Fourier Series It can be said, without overstating it, that any periodic signal of practical interest has a Fourier series. Only very strange periodic signals would not have a converging Fourier series. Establishing convergence is necessary because the Fourier series has ...
pointwise convergence of fourier series级数逐点收敛.pdf,Preface This book grew out of my attempt in August 1998 to compare Carleson’s and Fefferman’s proofs of the pointwise convergence of Fourier series with Lacey and Thiele’s proof of the boundedn
I'm reading Stein & Shakarchi's Fourier Analysis, but had a question about a small part of the proof of the mean-square convergence of fourier series of a function ff. To show the convergence, they first proved the Best Approximation Lemma, saying that fourier series is the best trigonome...
Let f be a piecewise continuous function defined on [-1, 1] with a full Fourier series given by a02+∑k=1∞(akcos(kπx)+bksin(kπx)). . converge to the function f ?” If we here refer to convergence in the mean square sense, then a partial answer to this question ...
Introduction to Fourier Series, including the definition of Fourier series, mean value convergence theorem, complex form of Fourier series, and links to Fourier series of some selected functions: rectangular waves, saw waves, etc.
Fischer. For Riemann integrals the Riesz-Fischer theorem is false. There are many convergence criteria for Fourier series, that is, sufficient conditions that guarantee the convergence of the series. The following condition, for example, is due to P. Dirichlet: if f(x) has a finite number of...
converge收敛(动,名)convergenta.convergencen. EquationsofMathematicalPhysicsECJTUZhuXu-sheng §2.1FOURIERSERIES Complex-valuedfunction 1,)()()( iixhxgxf fiscontinuous(differentiable,integrable)iffgandh arecontinuous(differentiable,integrable); iff=ifandonlyif ,)()()(,)()()( 222111 ixhxgxfixhxgxf ...
The main result is an mean convergence theorem for the partial sums of the Fourier series of a class function on a compact semi-simple Lie group. A central element in the proof is a Lie group-Lie algebra analog of the theorems in classic... RJ Stanton - 《Trans.amer.math.soc》 被引...
Strong Convergence Theorems for Two Parameter Vilenkin-Fourier Series. Acta Mathematica Hungarica 86, 17–38 (2000). https://doi.org/10.1023/A:1006787316897 Download citation Issue DateJanuary 2000 DOIhttps://doi.org/10.1023/A:1006787316897 Keywords Convergence Theorem Hardy Space Strong Convergence ...