Sum rules and constraints on passive systems
(2011) In Journal of Physics A: Mathematical and Theoretical20070101+01:00 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 wellknown
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 wellknown
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:
http://lup.lub.lu.se/record/1788854
 author
 Bernland, Anders ^{LU} ; Luger, Annemarie ^{LU} and Gustafsson, Mats ^{LU}
 organization
 publishing date
 2011
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Journal of Physics A: Mathematical and Theoretical20070101+01:00
 volume
 44
 issue
 14
 publisher
 IOP Publishing
 external identifiers

 wos:000288597500008
 scopus:79953706646
 ISSN
 17518113
 DOI
 10.1088/17518113/44/14/145205
 project
 EIT_HSWC:Antenna MIMO antennas and channels
 language
 English
 LU publication?
 yes
 id
 deb9845a25ea4a2e8aad103b2a6fa466 (old id 1788854)
 date added to LUP
 20110222 10:53:36
 date last changed
 20180107 10:15:59
@article{deb9845a25ea4a2e8aad103b2a6fa466, 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 wellknown<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 = {17518113}, language = {eng}, number = {14}, publisher = {IOP Publishing}, series = {Journal of Physics A: Mathematical and Theoretical20070101+01:00}, title = {Sum rules and constraints on passive systems}, url = {http://dx.doi.org/10.1088/17518113/44/14/145205}, volume = {44}, year = {2011}, }