Last updated January 29, 2005
This page lists old notes, etc., for Mth 627.
Expect some overlaps in the various files.
Eventually very old files will dribble off the bottom.
Many of the documents are in Portable Document Format (PDF).
You can use the free Adobe Acrobat Reader, available at
http://www.adobe.com, to view or print PDF files. The
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have reading or printing my PDF files.
The notes for Mth 627 are not complete. I may eventually get
around to editing and posting the remaining notes.
The sequence numbers in the note titles are just for keeping internal references
straight (maybe).
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2004 Winter Mth 627 0100 Weyl Quantization
PDF,
62 KB, 4 pages
-
This note gives an informal description of the Weyl quantization (1928) from the point
of view of pseudo-differential operators. It also gives a very nice example of the
breakdown of the group property of the exponential in the case of non-commuting exponents.
- 2004 Winter Mth 627 0055 Fourier Transform. L1 Theory
PDF, (to be posted later)
- This note defines the Fourier transfom on L1(Rn). We obtain the
standard inversion results that depend on a convergence factor. We also discuss the
classical theorems of Dini and Dirichlet which describe inversion of the transform by
conditionally convergent integrals, that is, by a Cauchy principal value at infinity.
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2004 Winter Mth 627 0035 Distributions with Compact Support
PDF,
70 KB, 5 pages
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We show that a distribution u with compact support K applied to a test function is
determined by the m-jet of the test function on K, where m is the order of the
distribution.We also give an example to show even if each k-jet of a sequence of test
functions vh converges uniformly to 0 on K it does not follow
that <u, vk> converges to 0. These results are from Laurent
Schwartz' text.
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2004 Winter Mth 627 0015 Convolution of Functions
PDF,
108 KB, 12 pages
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These notes discuss convolution of Lp functions, continuity of translation in
Lp and the du Bois-Reymond theorem (essentially the fundamental theorem of the
calculus of variations). The notes are a bit rough. Please let me know if you find any
errors or clumsiness.
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1998 Summer Mth 507 Graduate Seminar. Remarks on the Fourier Transform
PDF,
102 KB, 9 pages
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These notes are from the Summer Graduate Seminar, Mth 507, 1998. The notes are an
informal survey of some properties of the Fourier transform and a sketch of the
application to operational calculus of non-commuting operators.
Copyright © 2004 Bent E. Petersen. The documents
described here, may be used, copied and distributed
freely, entire and intact, for any educational noncommercial
purpose, but may not be distributed in an altered form. If you
want to improve on anything, which certainly can be
done, then please write your own version(s).
petersen@math.oregonstate.edu
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