Analytic representation

Xem 1-3 trên 3 kết quả Analytic representation

Đề tài " Analytic representation of functions and a new quasianalyticity threshold "

We characterize precisely the possible rate of decay of the anti-analytic half of a trigonometric series converging to zero almost everywhere. 1. Introduction 1.1. In 1916, D. E. Menshov constructed an example of a nontrivial trigonometric series on the circle T ∞ (1) n=−∞ c(n)eint which converges to zero almost everywhere (a.e.). Such series are called nullseries. This result was the origin of the modern theory of uniqueness in Fourier analysis, see [Z59], [B64], [KL87], [KS94]. Clearly for such a series |c(n)|2 = ∞.

33p noel_noel 17-01-2013 39 6 Download

SMOOTH AND DISCRETE SYSTEMS—ALGEBRAIC, ANALYTIC, AND GEOMETRICAL REPRESENTATIONS ˇ FRANTISEK

SMOOTH AND DISCRETE SYSTEMS—ALGEBRAIC, ANALYTIC, AND GEOMETRICAL REPRESENTATIONS ˇ FRANTISEK NEUMAN Received 12 January 2004 What is a diﬀerential equation? Certain objects may have diﬀerent, sometimes equivalent representations. By using algebraic and geometrical methods as well as discrete relations, diﬀerent representations of objects mainly given as analytic relations, diﬀerential equations can be considered.

10p sting12 10-03-2012 34 4 Download