Transcription of HARMONIC ANALYSIS - UCLA Mathematics
{{id}} {{{paragraph}}}
Example: marketing
HARMONIC ANALYSIS - UCLA Mathematics
HARMONIC ANALYSISTERENCE TAOA nalysis in general tends to revolve around the study of general classes offunc-tions(often real-valued or complex-valued) andoperators(which take one or morefunctions as input, and return some other function as output). HARMONIC analysis1focuses in particular on thequantitativeproperties of such functions, and how thesequantitative properties change when apply various (often quite explicit) good example of a quantitative property is for a functionf(x) being uniformlybounded in magnitude by an explicit upper boundM, or perhaps being squareintegrable with some boundA, thus |f(x)|2dx A. A typical question in har-monic ANALYSIS might then be the following: if a functionf:Rn Ris squareintegrable, and its gradient fexists and is also square integrable, does this implythatfis uniformly bounded?
many cases one deals primarily with special functions - polynomials, exponentials, trigonometric functions, and other very explicit and concrete functions. Such func-tions typically have a very rich algebraic and geometric structure, and there are many techniques from those fields of mathematics that can be used to give exact
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: