Banach algebras

Volker Pohl; Holger Boche

doi:10.1007/978-3-642-03639-2_3

Banach algebras

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Let L₁ be a linear system with transfer function f₁. An important task in applications is to find the transfer function f₂ of a second linear system L₂ such that the series connection of L₁ and L₂ has a prescribed transfer function f, i.e. such that f = f₁ f₂. If, for example, the desired transfer function f ≡ 1 is the identity then L₂ is the linear inverse system of L₁.

Original language	English
Title of host publication	Foundations in Signal Processing, Communications and Networking
Publisher	Springer Science and Business Media B.V.
Pages	51-66
Number of pages	16
DOIs	https://doi.org/10.1007/978-3-642-03639-2_3
State	Published - 2010
Externally published	Yes

Publication series

Name	Foundations in Signal Processing, Communications and Networking
Volume	4
ISSN (Print)	1863-8538
ISSN (Electronic)	1863-8546

Keywords

Banach Algebra
Banach Space
Division Algebra
Maximal Ideal
Unit Element

Access to Document

10.1007/978-3-642-03639-2_3

Cite this

@inbook{cd90ff99dae8412ca48ae2bf07f34eb6,

title = "Banach algebras",

abstract = "Let L1 be a linear system with transfer function f1. An important task in applications is to find the transfer function f2 of a second linear system L2 such that the series connection of L1 and L2 has a prescribed transfer function f, i.e. such that f = f1 f2. If, for example, the desired transfer function f ≡ 1 is the identity then L2 is the linear inverse system of L1.",

keywords = "Banach Algebra, Banach Space, Division Algebra, Maximal Ideal, Unit Element",

author = "Volker Pohl and Holger Boche",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2009.",

year = "2010",

doi = "10.1007/978-3-642-03639-2_3",

language = "English",

series = "Foundations in Signal Processing, Communications and Networking",

publisher = "Springer Science and Business Media B.V.",

pages = "51--66",

booktitle = "Foundations in Signal Processing, Communications and Networking",

}

TY - CHAP

T1 - Banach algebras

AU - Pohl, Volker

AU - Boche, Holger

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2009.

PY - 2010

Y1 - 2010

N2 - Let L1 be a linear system with transfer function f1. An important task in applications is to find the transfer function f2 of a second linear system L2 such that the series connection of L1 and L2 has a prescribed transfer function f, i.e. such that f = f1 f2. If, for example, the desired transfer function f ≡ 1 is the identity then L2 is the linear inverse system of L1.

AB - Let L1 be a linear system with transfer function f1. An important task in applications is to find the transfer function f2 of a second linear system L2 such that the series connection of L1 and L2 has a prescribed transfer function f, i.e. such that f = f1 f2. If, for example, the desired transfer function f ≡ 1 is the identity then L2 is the linear inverse system of L1.

KW - Banach Algebra

KW - Banach Space

KW - Division Algebra

KW - Maximal Ideal

KW - Unit Element

UR - http://www.scopus.com/inward/record.url?scp=85101076774&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-03639-2_3

DO - 10.1007/978-3-642-03639-2_3

M3 - Chapter

AN - SCOPUS:85101076774

T3 - Foundations in Signal Processing, Communications and Networking

SP - 51

EP - 66

BT - Foundations in Signal Processing, Communications and Networking

PB - Springer Science and Business Media B.V.

ER -

Banach algebras

Abstract

Publication series

Keywords

Access to Document

Other files and links

Fingerprint

Cite this