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Sum rules and constraints on passive systems

Bernland, Anders LU ; Luger, Annemarie LU and Gustafsson, Mats LU (2011) In Journal of Physics A: Mathematical and Theoretical 44(14).
Abstract
A passive system is one that cannot produce energy, a property that

naturally poses constraints on the system. A system in convolution form is fully described by its transfer function, and the class of Herglotz functions, holomorphic

functions mapping the open upper half plane to the closed upper half plane, is

closely related to the transfer functions of passive systems. Following a well-known

representation theorem, Herglotz functions can be represented by means of positive

measures on the real line. This fact is exploited in this paper in order to rigorously

prove a set of integral identities for Herglotz functions that relate weighted integrals

of the function to its... (More)
A passive system is one that cannot produce energy, a property that

naturally poses constraints on the system. A system in convolution form is fully described by its transfer function, and the class of Herglotz functions, holomorphic

functions mapping the open upper half plane to the closed upper half plane, is

closely related to the transfer functions of passive systems. Following a well-known

representation theorem, Herglotz functions can be represented by means of positive

measures on the real line. This fact is exploited in this paper in order to rigorously

prove a set of integral identities for Herglotz functions that relate weighted integrals

of the function to its asymptotic expansions at the origin and infinity.

The integral identities are the core of a general approach introduced here to derive

sum rules and physical limitations on various passive physical systems. Although

similar approaches have previously been applied to a wide range of specific applications,

this paper is the first to deliver a general procedure together with the necessary

proofs. This procedure is described thoroughly, and exemplified with examples from

electromagnetic theory. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Physics A: Mathematical and Theoretical
volume
44
issue
14
publisher
IOP Publishing
external identifiers
  • wos:000288597500008
  • scopus:79953706646
ISSN
1751-8113
DOI
10.1088/1751-8113/44/14/145205
project
EIT_HSWC:Antenna MIMO antennas and channels
language
English
LU publication?
yes
id
deb9845a-25ea-4a2e-8aad-103b2a6fa466 (old id 1788854)
date added to LUP
2011-02-22 10:53:36
date last changed
2017-04-09 04:33:19
@article{deb9845a-25ea-4a2e-8aad-103b2a6fa466,
  abstract     = {A passive system is one that cannot produce energy, a property that<br/><br>
naturally poses constraints on the system. A system in convolution form is fully described by its transfer function, and the class of Herglotz functions, holomorphic<br/><br>
functions mapping the open upper half plane to the closed upper half plane, is<br/><br>
closely related to the transfer functions of passive systems. Following a well-known<br/><br>
representation theorem, Herglotz functions can be represented by means of positive<br/><br>
measures on the real line. This fact is exploited in this paper in order to rigorously<br/><br>
prove a set of integral identities for Herglotz functions that relate weighted integrals<br/><br>
of the function to its asymptotic expansions at the origin and infinity.<br/><br>
The integral identities are the core of a general approach introduced here to derive<br/><br>
sum rules and physical limitations on various passive physical systems. Although<br/><br>
similar approaches have previously been applied to a wide range of specific applications,<br/><br>
this paper is the first to deliver a general procedure together with the necessary<br/><br>
proofs. This procedure is described thoroughly, and exemplified with examples from<br/><br>
electromagnetic theory.},
  articleno    = {145205},
  author       = {Bernland, Anders and Luger, Annemarie and Gustafsson, Mats},
  issn         = {1751-8113},
  language     = {eng},
  number       = {14},
  publisher    = {IOP Publishing},
  series       = {Journal of Physics A: Mathematical and Theoretical},
  title        = {Sum rules and constraints on passive systems},
  url          = {http://dx.doi.org/10.1088/1751-8113/44/14/145205},
  volume       = {44},
  year         = {2011},
}