جموعية متسلسلة فورييه المضاعفة و مرافقتها بطريقة نيورلند المضاعفة في الفضاء ([L-2 ([0,π]×[0,π

Abstract EN

Let f be a function of two variables U, V, periodic with respect to U and with respect to V, in each case with period 2n, and summable in the square Q: [—n,n] X [-n,n].

In this research we will proof two theorems.

The first study summability of the Double Fourier series 2m = 0 2n = 0 nAm n (u, v)to f at point (u, v) = (x, y) within a certain conditions, and we put the necessary lemmas for this theorem, and in the second we also study summability conjugate of the series: 2m=1 Zm=1[Smn cos mx cos ny — ymn sin mx cos ny — (3mn cos mx sin ny + amn sin mx sin ny] To [8]: f(x,y) = jniJo’' JOT ^(s't);anbidsdt 2 2 Where V(x,y) = ^(x,y;s,t) = 1 -{f(x + s,y + t) — f(x — s,y + t) — f(x + s,y — t) + f(x — s,y — t)} and put all necessary conditions and lemmas for this theorem by Double Norlund summability, which considered bounded linear operator, to both theorems in the space L2([0,n] X [0,n]).

and we can get many results, the most important of which is that the simple Fourier series or double Fourier Series, its Norlund summability to same function.

In conclusion, we can say that Double Norlund method are general rarely, follow up many methods as cesaro double and Holder Double and et.

This method has wide applications in analysis mathematics and spicily in approximation theory.