Alexits György: Convergence problems of orthogonal series (Budapest, 1961)
CONVEKGEJNCE PROBLEMS OF ORTHOGONAL SERIES by G. ALEXITS This volume gives a systematic account of the convergence theory of the orthogonal series. A revised and enlarged edition of the German original, it includes all the new and important discoveries of recent years. The questions of convergence and summation of the general orthogonal series form an impressive field of application of the Lesbesgue or of the Stieltjes—Lebesgue concept of integral. Many methods of enquiry owe their discovery to the investigation of this sphere of problems. Some of the results obtained give deeper knowledge of the convergence theorems, shaped specially to the expansion in question, even in cases of classical orthogonal expansions. This volume examines the actual state of the theory of convergence and summation of the general orthogonal series. It also shows the connection of the general theory with the corresponding questions of classical expansion.