62
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

A transform of finite order entire functions and perturbations of zeros

Pages 493-509 | Received 10 Sep 2008, Accepted 20 Jan 2009, Published online: 08 May 2009

References

  • Berenstein , C and Gay , R . 1995 . Complex Analysis and Special Topics in Harmonic Analysis , New York : Springer-Verlag .
  • Rosenbloom , PC . 1969 . Perturbation of zeros of analytic functions. I . J. Approx. Theory , 2 : 111 – 126 .
  • Saks , S and Zygmund , A . 1965 . Analytic Functions , Warszawa : Polish Science Publishers .
  • Edrei , A , Saff , EB and Varga , RS . 1983 . “ Zeros of Sections of Power Series ” . In Lecture Notes in Mathematics, 1002 , Berlin : Springer-Verlag .
  • Ganelius , T . 1963 . The zeros of partial sums of power series . Duke Math. J. , 30 : 533 – 540 .
  • Ostrovskii , IV . 2000 . On the zeros of tails of power series . Oper. Theory Ad. Appl. , 113 : 279 – 285 .
  • Yildirim , CY . 1994 . On the tails of exponential series . Can. Math. Bull , 37 : 278 – 286 .
  • Clunie , JG and Edrei , A . 1991 . Zeros of successive derivatives of analytic functions having a single essential singularity. II . J. Anal. Math. , 56 : 141 – 185 .
  • Craven , T , Csordas , G and Smith , W . 1987 . Zeros of derivatives of entire functions . Proc. Amer. Math. Soc. , 101 : 323 – 326 .
  • Edwards , S and Hellerstein , S . 2002 . Non-real zeros of derivatives of real entire functions and the Polya–Wiman conjectures . Compl Var., Theory Appl. , 47 ( 1 ) : 25 – 57 .
  • Genthner , RM . 1985 . On the zeros of the derivatives of some entire functions of finite order . Proc. Edinb. Math. Soc., II. Ser. , 28 : 381 – 407 .
  • Harel , A , Namn , S and Sturm , J . 1999 . Migration of zeros for successive derivatives of entire functions . Proc. Am. Math. Soc. , 127 ( 2 ) : 563 – 567 .
  • Sheil-Small , T . 1989 . On the zeros of the derivatives of real entire functions and Wiman's conjecture . Ann. Math.(2) , 129 ( 1 ) : 179 – 193 .
  • Ram Murty , M . 2001 . Problems in Analytic Number Theory , Berlin : Springer .
  • Gil' , MI . 2003 . “ Operator Functions and Localization of Spectra ” . In Lectures Notes in Mathematics , Vol. 1830 , Berlin : Springer-Verlag .
  • Gil , MI . 2007 . Bounds for zeros of entire functions . Acta Appl. Math. , 99 : 117 – 159 .
  • Milovanovic´ , GV , Mitrinovic´ , DS and Rassias , ThM . 1994 . Topics in Polynomials: Extremal Problems, Inequalities, Zeros , Singapore : World Scientific .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.