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?)
