Stochastic and Multiscale Modeling and Computation Seminar by Aleksei Sorokin: Walsh Functions and Spaces

Speaker: Aleksei Sorokin, Illinois Institute of Technology

Title: Walsh Functions and Spaces

Abstract: The Fourier series expands a periodic function into a sum of trigonometric functions. For smooth periodic functions, the Fourier coefficients decay rapidly with some regularity. In this talk, we explore the Walsh functions which form a complete orthonormal system in L2([0,1)) without requiring periodicity in the function. Like the Fourier coefficients, when a function is known to have a certain smoothness, we can say something about the decay of its Walsh coefficients. Spaces of smooth periodic functions derived from decays of Fourier coefficients and spaces containing smooth functions derived from the decay of the Walsh coefficients are explored. The speaker makes connections to his research at the intersection of kernel methods and Quasi-Monte Carlo.

This is a joint seminar between the Computational Math and Stats group and the Multiscale group. 

Stochastic and Multiscale Modeling and Computation Seminar