Entire Approximations for a Class of Truncated and Odd Functions

被引：7

作者：

Carneiro, Emanuel ^{[1
]}

Littmann, Friedrich ^{[2
]}

机构：

[1] IMPA, BR-22460320 Rio De Janeiro, Brazil

[2] N Dakota State Univ, Dept Math, Fargo, ND 58105 USA

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2013年 / 19卷 / 05期

关键词：

Truncated functions; Truncated logarithm; Exponential type; Extremal functions; Minorants; EXTREMAL-FUNCTIONS; ZETA-FUNCTION; ZEROS;

D O I：

10.1007/s00041-013-9273-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We solve the problem of finding optimal entire approximations of prescribed exponential type (unrestricted, majorant and minorant) for a class of truncated and odd functions with a shifted exponential subordination, minimizing the -error. The class considered here includes new examples such as the truncated logarithm and truncated shifted power functions. This paper is the counterpart of the works (Carneiro and Vaaler in Trans. Am. Math. Soc. 362:5803-5843, 2010) and (Carneiro and Vaaler in Constr. Approx. 31(2):259-288, 2010) where the analogous problem for even functions was treated.

引用

页码：967 / 996

页数：30

共 22 条

[1] Note on a diophantine inequality in several variables
Barton, JT
Montgomery, HL
Vaaler, JD
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (02) : 337 - 345
[2] Bandlimited Approximations to the Truncated Gaussian and Applications
Carneiro, Emanuel
Littmann, Friedrich
[J]. CONSTRUCTIVE APPROXIMATION, 2013, 38 (01) : 19 - 57
[3] GAUSSIAN SUBORDINATION FOR THE BEURLING-SELBERG EXTREMAL PROBLEM
Carneiro, Emanuel
Littmann, Friedrich
Vaaler, Jeffrey D.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 365 (07) : 3493 - 3534
[4] SOME EXTREMAL FUNCTIONS IN FOURIER ANALYSIS. II
Carneiro, Emanuel
Vaaler, Jeffrey D.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 362 (11) : 5803 - 5843
[5] Bounding ζ (s) in the critical strip
Carneiro, Emanuel
Chandee, Vorrapan
[J]. JOURNAL OF NUMBER THEORY, 2011, 131 (03) : 363 - 384
[6] Some Extremal Functions in Fourier Analysis, III
Carneiro, Emanuel
Vaaler, Jeffrey D.
[J]. CONSTRUCTIVE APPROXIMATION, 2010, 31 (02) : 259 - 288
[7] Bounding |ζ(1/2+it)| on the Riemann hypothesis
Chandee, Vorrapan
Soundararajan, K.
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2011, 43 : 243 - 250
[8] GALLAGHER PX, 1985, J REINE ANGEW MATH, V362, P72
[9] Ganzburg M. I, 2010, J CONCR APPL MATH, V8, P208
[10] A note on S(t) and the zeros of the riemann zeta-function
Goldston, D. A.
Gonek, S. M.
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2007, 39 : 482 - 486

← 1 2 3 →