| Explorations in Harmonic Analysis: With Applications to Complex Function Theory and the Heisenberg Group 2009 Edition Contributor(s): Krantz, Steven G. (Author) |
|
 |
ISBN: 081764668X ISBN-13: 9780817646684 Publisher: Birkhauser OUR PRICE: $52.24 Product Type: Hardcover Published: May 2009 |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Group Theory - Mathematics | Differential Equations - General |
| Dewey: 515.243 |
| LCCN: 2009926530 |
| Series: Applied and Numerical Harmonic Analysis |
| Physical Information: 0.88" H x 6.14" W x 9.21" (1.55 lbs) 362 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Harmonic analysis is a venerable part of modern mathematics. Its roots began, perhaps, with late eighteenth-century discussions of the wave equation. Using the method of separation of variables, it was realized that the equation could be solved with a data function of the form?(x)= sin jx for j? Z.Itwasnaturaltoask, using the philosophy of superposition, whether the equation could then be solved with data on the interval [0, ?] consisting of a nite linear combinationof the sin jx. With an af rmative answer to that question, one is led to ask about in?nite linear combinations. This was an interesting venue in which physical reasoning interacted with mathematical reasoning. Physical intuition certainly suggests that any continuous function? can be a data function for the wave equation. So one is led to ask whether any continuous? can be expressed as an (in nite) superposition of sine functions. Thus was born the fundamental question of Fourier series. No less an eminence gris than Leonhard Euler argued against the proposition |