000			01640nam a2200229 4500
001			13527775
010			_a 2004104246
020			_a354021058X (acidfree paper)
082	0	0	_a515.24 _bKOR/T
100	1		_aKorevaar, Jacob
245	1	0	_aTauberian theory : _ba century of developments
260			_aBerlin _bSpringer _c2004.
300			_axv, 483 p : _bill. ;
520			_aTauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the beginning and his expert commentary evokes the excitement surrounding the early results. He shows the fascination of the difficult Hardy-Littlewood theorems and of an unexpected simple proof, and extolls Wiener's breakthrough based on Fourier theory. There are the spectacular "high-indices" theorems and Karamata's "regular variation", which permeates probability theory. The author presents Gelfand's elegant algebraic treatment of Wiener theory and his own distributional approach. There is also a new unified theory for Borel and "circle" methods. The text describes many Tauberian ways to the prime number theorem. A large bibliography and a substantial index round out the book
650		0	_aTauberian theorems
650		0	_aSummability theory
650		0	_aHardy-Littlewood method
856	4	2	_uhttp://www.loc.gov/catdir/enhancements/fy0817/2004104246-b.html
856	4	2	_uhttp://www.loc.gov/catdir/enhancements/fy0817/2004104246-d.html
856	4	1	_uhttp://www.loc.gov/catdir/enhancements/fy0817/2004104246-t.html
942			_cBK
999			_c66833 _d66833