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.