Probility and the (C,r) summability of Fourier series

The aim of this study which compose of eight parts, is to investigate probability and the (C,r) summability of Fourier series. In the first chapter, information about the historical development of the relation ship (C,r)summability of Fourier series and probability is given. In the second chapter, the proof of theorems with respect to the state space R and the random walk is investigated. In the third chapter, the proof of theorems with respect to regular and superregular functions is investigated. In the fourth chapter, the proof of theorems with respect to h -path processes is investigated. In the fifth chapter, the proof of theorems with respect to the Martin exit boundary of the Markov chains investigated. In the sixth chapter, the proof of theorems with respect to Martin representation theorem and the class of minimal regular functions is investigated. In the seventh chapter, the proof of theorems with respect to resolutivity of the boundaryR^'is investigated. In the eighth chapter, the proof of theorems with respect to boundary behavior of nonnegativeh - superregular functions is investigated