William R. Wade Professor  Department of  Mathematics  University of  Tennessee Knoxville, TN 37996-1320 865-974-4320 (Office) 865-974-6576 (Fax) wade@math.utk.edu

  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 piece-wise constant components by generating numbers (called Walsh-Fourier coefficients) and infinite series (Walsh-Fourier 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 Walsh-Fourier coefficients of a some integrable function?) and growth (how fast do the partial sums or the Cesaro means of a Walsh-Fourier series grow?). Specific results can be obtained by looking at the papers in my bibliography.

Dyadic Harmonic analysis has many applications. Using Walsh-Fourier 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 Walsh-Fourier coefficients to characterize functions makes it possible to recognize patterns (e.g., read handwritten zip-codes). Walsh functions have also been used to design genetic algorithms, methods to optimize non-differentiable 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, Pio-Rivera), 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 Polish-American 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

    Curriculum vitae

        Misprints for:

• "An Introduction to Analysis" (Misprints (misprints in the 1st printing of the 4th ed.)), Prentice Hall, 2004, ISBN#0-13-145333-5.
• Walsh Series: An Introduction to Dyadic Harmonic Analysis", (with F. Schipp, P. Simon, and J.Pal), Adam Hilger Ltd, 1990, ISBN#0-7503-0068-X. Now available from classbook.com.

Teaching Schedule

Fall 2011:
     Math 300 Syllabus (pdf file)
     Math 341 Syllabus (pdf file)   

email address:  wade@math.utk.edu

Last updated: 7/11
pha