William R. Wade Professor 

Research Interests
I do research on Dyadic Harmonic Analysis. This area, whose roots lie in the physics of vibration, uses integration to decompose (integrable) functions into piecewise constant components by generating numbers (called WalshFourier coefficients) and infinite series (WalshFourier series). These numbers and series can be used to approximate and to characterize the original function. I am particularly interested in problems of uniqueness (under which conditions are the coefficients of an otherwise arbitrary Walsh series the WalshFourier coefficients of a some integrable function?) and growth (how fast do the partial sums or the Cesaro means of a WalshFourier series grow?). Specific results can be obtained by looking at the papers in my bibliography.
Dyadic Harmonic analysis has many applications. Using WalshFourier series to approximate a given function makes it possible to transmit data efficiently (e.g., multiplexing), to filter data (e.g., remove noise from weak video signals), and for data compression (e.g., transmit hundreds of signals through a single fiber optic cable). Using WalshFourier coefficients to characterize functions makes it possible to recognize patterns (e.g., read handwritten zipcodes). Walsh functions have also been used to design genetic algorithms, methods to optimize nondifferentiable problems for which the standard approach via calculus will not work.
I am also interested in Math History. I enjoy discovering how concepts were discovered and what purposes they serve in the 21st century. I use this material to make myself a better teacher, and to enliven my course in Math History.
Short Biography
I was born in downtown Los Angeles on sixth street (they still had houses there in the early forties). Moving steadily east (East Los Angeles, Montebello, PioRivera), we ended in La Puente. I graduated from Puente High School in June 1961. I spent the next seven years getting three degrees at the University of California (Riverside). My Ph.D. Advisor was V.L. Shapiro, a student of the famed PolishAmerican analyst A . Zygmund.
I have taught at the University of Tennessee since September 1968, where I have had six Ph.D. students, and have received various honors, awards and grants over the years, and have been on leave at the University of Southern California (spring, 1977), Moscow State University (Fall 1977), Indian Statistical Institute (Spring 1984), and Eotvos Lorand University, Budapest (Summers 1985, 1990, 1995, 1999).
Selected Bibliography
Books in PrintMisprints for:
Teaching
Schedule
Fall 2011:
Math 300 Syllabus (pdf file)
Math 341 Syllabus (pdf file)
Egypt

Hong Kong

Hungary

India

Knoxville

Russia

* Pyramids
* Cairo 

California  Italy  Majorca  
email address: wade@math.utk.edu
Last updated: 7/11
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