By Y. Okuyama

**Read Online or Download Absolute Summability Of Fourier Series And Orthogonal Series PDF**

**Similar linear books**

**The Symmetric Eigenvalue Problem (Classics in Applied Mathematics)**

A droll explication of innovations that may be utilized to appreciate a few of crucial engineering difficulties: these facing vibrations, buckling, and earthquake resistance. whereas containing huge thought, this can be an utilized arithmetic textual content that reads as though you're eavesdropping at the writer speaking out loud to himself.

**Signal Enhancement with Variable Span Linear Filters**

This ebook introduces readers to the unconventional proposal of variable span speech enhancement filters, and demonstrates the way it can be utilized for powerful noise aid in a variety of methods. extra, the publication offers the accompanying Matlab code, permitting readers to simply enforce the most principles mentioned. Variable span filters mix the guidelines of optimum linear filters with these of subspace equipment, as they contain the joint diagonalization of the correlation matrices of the specified sign and the noise.

- Álgebra Lineal y Algunas de sus Aplicaciones
- Extensions of Linear-Quadratic Control, Optimization and Matrix Theory
- Semi-Simple Lie Algebras and Their Representations (Dover Books on Mathematics)
- Boundary Value Problems for Linear Evolution Partial Differential Equations: Proceedings of the NATO Advanced Study Institute held in Liège, Belgium, September 6–17, 1976
- Abstract Root Subgroups and Simple Groups of Lie-Type
- Quaternions, Spinors, and Surfaces

**Additional resources for Absolute Summability Of Fourier Series And Orthogonal Series**

**Example text**

5), we have easily the following corollary. 2. 13) For the trigonometric system, we shall make a remark. 2) in Chapter 3. 2, we have the following corollary. 3. 1. (i) If ~ >0 and ~( 6,f) = 0(Ls(i/6)-a/2L~0)_ (I/6)~(E)~1/6)-1) Lp+s~ for some s >0, then the Fourier series n=[0An(X) is summable IR,exp Ls(n)~,l I almost everywhere. (ii) If ~ > 0 and n(6,f) = 0(LI(I/6)I/2L (C ) (1/6 )-1) P for some s >0, then the Fourier series [ An(X) is smnmable n=0 42 IR,na,ll almost (iil) everywhere. 4. 5, these =[0An(X) integral moduli Rademacher Trigonometric Series.

2. of Varshney Let {pn } be non-negative t > 0, be a positive, non-decreasing [87], Kanno [34] proved and non-increasing. function satisfying the Let the con- dition {In/P n} is non-increaslng. If the conditions k=n Pklk 2 Pk 1 = 0(~ -), n : 0 , 1 , 2 , . . 5) I~ l(C/t)Id¢(t) I < ~ 0 for some constant C > 0 hold, then the series (n+l)p n Pn XnAn+l(t) n=0 is summable IN,Pnl , at t =x. 2. Summability the following Now we generalize these above theorems in form. Theorem that Factors. of these theorems.

4) converges for some ¢ > 0, then the series [ an#n(X) is summable IR,Ls(n)e, ll almost everywhere. (v) If ~ > 0 and the series [lanI2n Ls(n) -~ (¢). 5) Lp+s(n) converges for some ¢ > 0, then the series [ anOn(X) is summable IR,exp n/Ls(n)~,iI almost everywhere. Proof. As these results are analogously proved, we shall prove here only the case (i). i~(n)p~ { [ ~ [ n n=k X Pk-1 2 p2 n=l n p2 p2 n n-i 2 1/2 lakl } k=l n-i L(e) (n) 2 p+s Pn n 1/2 } On the other hand, if we put Pn = exp Ls(n)~ , we see that Pn ~ n-iLs (n) ~L~0) (n) -lexp Ls(n)~ .