02906nmm a2200373 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002200139245010000161250001700261260004800278300003200326505027400358653003200632653002600664653002100690653003500711653003400746653004900780653001900829653002800848653002500876653002100901041001900922989003800941490003700979028003001016856007201046082001401118520140001132EB000710650EBX0100000000000000135021200000000000000.0cr|||||||||||||||||||||140122 ||| eng a97894009028311 aZhizhiashvili, L.00aTrigonometric Fourier Series and Their ConjugateshElektronische Ressourcecby L. Zhizhiashvili a1st ed. 1996 aDordrechtbSpringer Netherlandsc1996, 1996 aXII, 308 pbonline resource0 aPreface -- 1 Simple Trigonometric Series -- I. The Conjugation Operator and the Hilbert Transform -- II. Pointwise Convergence and Summability of Trigonometric Series -- III. Convergence and Summability of Trigonometric Fourier Series and Their Conjugates in the Spaces aFunctions of real variables aMathematical analysis aFourier Analysis aSequences, Series, Summability aApproximations and Expansions aIntegral Transforms and Operational Calculus aReal Functions aSequences (Mathematics) aApproximation theory aFourier analysis07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aMathematics and Its Applications50a10.1007/978-94-009-0283-140uhttps://doi.org/10.1007/978-94-009-0283-1?nosfx=yxVerlag3Volltext0 a5,152,433 aResearch in the theory of trigonometric series has been carried out for over two centuries. The results obtained have greatly influenced various fields of mathematics, mechanics, and physics. Nowadays, the theory of simple trigonometric series has been developed fully enough (we will only mention the monographs by Zygmund [15, 16] and Bari [2]). The achievements in the theory of multiple trigonometric series look rather modest as compared to those in the one-dimensional case though multiple trigonometric series seem to be a natural, interesting and promising object of investigation. We should say, however, that the past few decades have seen a more intensive development of the theory in this field. To form an idea about the theory of multiple trigonometric series, the reader can refer to the surveys by Shapiro [1], Zhizhiashvili [16], [46], Golubov [1], D'yachenko [3]. As to monographs on this topic, only that ofYanushauskas [1] is known to me. This book covers several aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions; convergence (pointwise and in the LP-norm, p > 0) of Fourier series and their conjugates, as well as their summability by the Cesaro (C,a), a> -1, and Abel-Poisson methods; approximating properties of Cesaro means of Fourier series and their conjugates