The second volume contains Obrechkoffs works in one of the most actively elaborated regions of investigations in the classical analysis in the 20th century. Deep results for the summation of the Taylor, Dirichlet, Fourier and Laplace series by means of the classical method of Riemann, Cesaro, Riesz, Euler-Knopp, Borel, Mittag-Leffler and Hausdorff are included. For the first time is studied the summation of Taylors series of a function, holomorphic at the origin, at points on the boundary of its Borels polygon of summation. An absolute summation by typical Riesz means is introduced and applied to the classical Dirichlet ... |
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Книга 7 от поредицата "Bulgarian Academic Monographs". ... This book is the second edition of a book with the same title, but in Bulgarian, published in 1963. Nikola Obrechkoff (1896 – 1963) was a world renowned specialist in the field of the geometry of polynomials. To him are due outstanding generalizations of the Descartes rule, Budan – Fourier theorem, and of several Laguerre’s theorems. In his last publication On some algebraic covariants and the zeros of polynomials he proposed a very promising new approach to the classicial item of the localization of the zeros of polynomials. Unfortunately, this ... |
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