Lattice Quantum Field Theory

Fourier Theory on the Complex Plane

by Jorge L. deLyra

This is version 1 of this page. The version reflects the state of the scientific content. The page may be updated at any time for the correction of small errors of for small improvements, in either case with no relevant bearing on the content. This page was last updated on Fri Jan 8 11:45:49 UTC 2016.

This page is separated into five parts, numbered as I, II, III, IV and V:
I: Conjugate Pairs of Fourier Series and Inner Analytic Functions
II: Weak Convergence, Classification and Factorization of Singularities
III: Low-Pass Filters, Singularity Splitting and Infinite-Order Filters
IV: Representability of Real Functions by their Fourier Coefficients
V: Arbitrary-Parity Real Functions, Singular Generalized Functions and Locally Non-Integrable Functions

You can read the page online in HTML-I - HTML-II - HTML-III - HTML-IV - HTML-V format, or download a copy in either PDF-I (size: 326 kB) - PDF-II (size: 336 kB) - PDF-III (size: 609 kB) - PDF-IV (size: 142 kB) - PDF-V (size: 274 kB) format or PS-I (size: 1090 kB) - PS-II (size: 1085 kB) - PS-III (size: 4397 kB) - PS-IV (size: 459 kB) - PS-V (size: 652 kB) format. Note that the HTML version is not guaranteed to be perfectly formatted, while the PS and PDF versions should be perfect. If you have the appropriate PDF plug-in in your browser, you should be able to read the PDF-I version online - PDF-II version online - PDF-III version online - PDF-IV version online - PDF-V version online ; if this version does not appear in your browser at the first trial, and a blank page shows up instead, just reload; sometimes the browser is a bit sluggish to load the plugin. If you have your browser configured to use a PS viewer existing in your system, you should be able to read the PS-I version on your screen - PS-II version on your screen - PS-III version on your screen - PS-IV version on your screen - PS-V version on your screen .

If you decide to print a copy, please note that the page is formatted for A4 paper in one-sided format, that part I has a total of 44 pages, including 19 pages of appendices, that part II has a total of 43 pages, including 20 pages of appendices, that part III has a total of 44 pages, including 17 pages of appendices, that part IV has a total of 13 pages, including 3 pages of appendices, and that part V has a total of 32 pages, including 3 pages of appendices.

You can also obtain here a compressed tar file with the source code relating to this page: FTOTCP-III.tar.bz2. Note that, although there is a makefile within the src/ directory extracted from the tar file, just typing "make" will not work. In order to compile and execute the programs you will have to read the files within the directory and understand what they are and how they work. Reading the README file found in the src/ directory might help.

JLdL 08Jan16