Extension of Inverses of Entire Functions of Genus 1 and 2 to the Upper Half Plane

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Extension of Inverses of Entire Functions of Genus 1 and 2 to the Upper Half Plane. / Pedersen, Henrik Laurberg.

I: Computational Methods and Function Theory, Bind 13, Nr. 2, 2013, s. 263-275.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Pedersen, HL 2013, 'Extension of Inverses of Entire Functions of Genus 1 and 2 to the Upper Half Plane', Computational Methods and Function Theory, bind 13, nr. 2, s. 263-275. https://doi.org/10.1007/s40315-013-0020-4

APA

Pedersen, H. L. (2013). Extension of Inverses of Entire Functions of Genus 1 and 2 to the Upper Half Plane. Computational Methods and Function Theory, 13(2), 263-275. https://doi.org/10.1007/s40315-013-0020-4

Vancouver

Pedersen HL. Extension of Inverses of Entire Functions of Genus 1 and 2 to the Upper Half Plane. Computational Methods and Function Theory. 2013;13(2):263-275. https://doi.org/10.1007/s40315-013-0020-4

Author

Pedersen, Henrik Laurberg. / Extension of Inverses of Entire Functions of Genus 1 and 2 to the Upper Half Plane. I: Computational Methods and Function Theory. 2013 ; Bind 13, Nr. 2. s. 263-275.

Bibtex

@article{11e59a1d8a3c4f53b3c885d62c208626,
title = "Extension of Inverses of Entire Functions of Genus 1 and 2 to the Upper Half Plane",
abstract = "Any entire function of genus 1 which is positive on the positive real axis and which has only negative zeros decreases on some unbounded interval of the positive axis. The inverse of its reciprocal is shown to have an extension from that interval to a Pick-function in the upper half plane. A similar result holds for a class of entire functions of genus 2 and in particular the inverse function of Barnes{\textquoteright} double gamma function on a certain interval of the positive axis can be extended to a Pick-function. These results are proved using positive and negative definite kernels.",
author = "Pedersen, {Henrik Laurberg}",
year = "2013",
doi = "10.1007/s40315-013-0020-4",
language = "English",
volume = "13",
pages = "263--275",
journal = "Computational Methods and Function Theory",
issn = "1617-9447",
publisher = "Springer",
number = "2",

}

RIS

TY - JOUR

T1 - Extension of Inverses of Entire Functions of Genus 1 and 2 to the Upper Half Plane

AU - Pedersen, Henrik Laurberg

PY - 2013

Y1 - 2013

N2 - Any entire function of genus 1 which is positive on the positive real axis and which has only negative zeros decreases on some unbounded interval of the positive axis. The inverse of its reciprocal is shown to have an extension from that interval to a Pick-function in the upper half plane. A similar result holds for a class of entire functions of genus 2 and in particular the inverse function of Barnes’ double gamma function on a certain interval of the positive axis can be extended to a Pick-function. These results are proved using positive and negative definite kernels.

AB - Any entire function of genus 1 which is positive on the positive real axis and which has only negative zeros decreases on some unbounded interval of the positive axis. The inverse of its reciprocal is shown to have an extension from that interval to a Pick-function in the upper half plane. A similar result holds for a class of entire functions of genus 2 and in particular the inverse function of Barnes’ double gamma function on a certain interval of the positive axis can be extended to a Pick-function. These results are proved using positive and negative definite kernels.

U2 - 10.1007/s40315-013-0020-4

DO - 10.1007/s40315-013-0020-4

M3 - Journal article

VL - 13

SP - 263

EP - 275

JO - Computational Methods and Function Theory

JF - Computational Methods and Function Theory

SN - 1617-9447

IS - 2

ER -

ID: 95307019