Realization of tensor product and of tensor factorization of rational functions

Daniel Alpay; Izchak Lewkowicz

doi:10.1007/s40509-019-00190-w

Realization of tensor product and of tensor factorization of rational functions

Daniel Alpay, Izchak Lewkowicz

Department of Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We study the state space realization of a tensor product of a pair of rational functions. At the expense of “inflating” the dimensions, we recover the classical expressions for realization of a regular product of rational functions. Under an additional assumption that the limit at infinity of a given rational function exists and is equal to identity, we introduce an explicit formula for a tensor factorization of this function.

Original language	English
Pages (from-to)	269-278
Number of pages	10
Journal	Quantum Studies: Mathematics and Foundations
Volume	6
Issue number	3
DOIs	https://doi.org/10.1007/s40509-019-00190-w
State	Published - 1 Sep 2019

Keywords

Factorization of rational functions
State space realization
Tensor product

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics
Mathematical Physics

Access to Document

10.1007/s40509-019-00190-w

Cite this

@article{07858b2ee5c941028c4f14a8ffc4ff66,

title = "Realization of tensor product and of tensor factorization of rational functions",

abstract = "We study the state space realization of a tensor product of a pair of rational functions. At the expense of “inflating” the dimensions, we recover the classical expressions for realization of a regular product of rational functions. Under an additional assumption that the limit at infinity of a given rational function exists and is equal to identity, we introduce an explicit formula for a tensor factorization of this function.",

keywords = "Factorization of rational functions, State space realization, Tensor product",

author = "Daniel Alpay and Izchak Lewkowicz",

note = "Publisher Copyright: {\textcopyright} 2019, Chapman University.",

year = "2019",

month = sep,

day = "1",

doi = "10.1007/s40509-019-00190-w",

language = "English",

volume = "6",

pages = "269--278",

journal = "Quantum Studies: Mathematics and Foundations",

issn = "2196-5609",

publisher = "Birkhaeuser",

number = "3",

}

TY - JOUR

T1 - Realization of tensor product and of tensor factorization of rational functions

AU - Alpay, Daniel

AU - Lewkowicz, Izchak

PY - 2019/9/1

Y1 - 2019/9/1

N2 - We study the state space realization of a tensor product of a pair of rational functions. At the expense of “inflating” the dimensions, we recover the classical expressions for realization of a regular product of rational functions. Under an additional assumption that the limit at infinity of a given rational function exists and is equal to identity, we introduce an explicit formula for a tensor factorization of this function.

AB - We study the state space realization of a tensor product of a pair of rational functions. At the expense of “inflating” the dimensions, we recover the classical expressions for realization of a regular product of rational functions. Under an additional assumption that the limit at infinity of a given rational function exists and is equal to identity, we introduce an explicit formula for a tensor factorization of this function.

KW - Factorization of rational functions

KW - State space realization

KW - Tensor product

UR - http://www.scopus.com/inward/record.url?scp=85091761284&partnerID=8YFLogxK

U2 - 10.1007/s40509-019-00190-w

DO - 10.1007/s40509-019-00190-w

M3 - Article

AN - SCOPUS:85091761284

SN - 2196-5609

VL - 6

SP - 269

EP - 278

JO - Quantum Studies: Mathematics and Foundations

JF - Quantum Studies: Mathematics and Foundations

IS - 3

ER -

Realization of tensor product and of tensor factorization of rational functions

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this