Date of Graduation
Master of Science in Mathematics
uniform distribution, sequence, Wehl criterion, Fejér, double sequence
In this thesis, we study the theory of uniform distribution of sequences of real numbers. We first give an exposition of the necessary mathematical tools including a rare type of Mean-Value Theorems, Fourier series, Fourier transforms, and the uniform boundedness of sequences of functions. We devote the main body of the thesis to prove theorems based on the well-known Weyl's Criterion and investigate their applications. In particular, we prove and utilize Fejer's Theorem to determine the uniform distribution of several single and double sequences. The contribution of this can be mainly manifested in its thoroughness and completeness of the proofs provided which, in our opinion, is lacking or inaccessible in the current literature. The effort undertaken here will help practitioners to fully understand the intricacy of the theory and enable them to master its applications. Furthermore, we use alternative ways to analyze a few examples, which will facilitate implementation of these mathematical methods.
© Stacy Jo Robinson
Robinson, Stacy Jo, "An Introduction to Uniform Distribution Modulo 1" (2011). MSU Graduate Theses. 2524.