Analytic representation

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 38 6   Download

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 30 4   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Nhiễu loạn phân tích của $ \ bar \ một phần $-nhà điều hành và các công thức đại diện không thể thiếu trong không gian Hilbert...

19p matuot_266 26-08-2011 71 5   Download

In modern high-performance liquid chromatography (HPLC), computers in a broad sense are used in every instrumental module and at every stage of analysis. Computers control the flow rate, eluent composition, temperature, injection volume, and injection process. Detector output signal is converted from analog form into the digital representation to recognize the presence of peaks, and then at higher level of computer analysis a chromatogram is obtained. All these computer-based functions are performed in the background, and the chromatographer usually does not think about them.

30p bigbaby87 03-09-2010 120 20   Download

PROCESS, QUANTUM, AND ANALYTICAL SENSORS INTRODUCTION Automatic test systems, manufacturing process control, analytical instrumentation, and aerospace electronic systems all would have diminished capabilities without the availability of contemporary computer integrated data systems with multisensor information structures. This text develops supporting quantitative error models that enable a unified performance evaluation for the design and analysis of linear and digital instrumentation systems with the goal of compatibility of integration with other enterprise quality representations....

23p huggoo 20-08-2010 89 4   Download