A Hilbert space approach to difference equations

Konrad Kitzing; Rainer Picard; Stefan Siegmund; Sascha Trostorff; Marcus Waurick

doi:10.1007/978-3-030-20016-9_12

A Hilbert space approach to difference equations

Konrad Kitzing, Rainer Picard, Stefan Siegmund^*, Sascha Trostorff, Marcus Waurick

^*Corresponding author for this work

Mathematics And Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

1 Citation (Scopus)

Abstract

We consider general difference equations u_n₊₁= F(u) _n for n∈ Z on exponentially weighted ℓ₂ spaces of two-sided Hilbert space-valued sequences u and discuss initial value problems. As an application of the Hilbert space approach, we characterize exponential stability of linear equations and prove a stable manifold theorem for causal nonlinear difference equations.

Original language	English
Title of host publication	Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 23, 2017
Editors	Saber Elaydi, Christian Pötzsche, Adina Luminiţa Sasu
Publisher	Springer New York
Pages	285-307
Number of pages	23
Volume	287
ISBN (Print)	9783030200152
DOIs	https://doi.org/10.1007/978-3-030-20016-9_12
Publication status	Published - 30 Jun 2019
Event	23rd International Conference on Difference Equations and Applications, ICDEA 2017 - Timişoara, Romania Duration: 24 Jul 2017 → 28 Jul 2017

Conference

Conference	23rd International Conference on Difference Equations and Applications, ICDEA 2017
Country/Territory	Romania
City	Timişoara
Period	24/07/17 → 28/07/17

Keywords

causality
exponential stability
exponentially weighted spaces
non-linear difference equations
stable manifold theorem
Z transform

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10.1007/978-3-030-20016-9_12

Cite this

@inproceedings{d76584e65f7142d18565b2cff5f7e256,

title = "A Hilbert space approach to difference equations",

abstract = "We consider general difference equations un+1= F(u) n for n∈ Z on exponentially weighted ℓ2 spaces of two-sided Hilbert space-valued sequences u and discuss initial value problems. As an application of the Hilbert space approach, we characterize exponential stability of linear equations and prove a stable manifold theorem for causal nonlinear difference equations.",

keywords = "causality, exponential stability, exponentially weighted spaces, non-linear difference equations, stable manifold theorem, Z transform",

author = "Konrad Kitzing and Rainer Picard and Stefan Siegmund and Sascha Trostorff and Marcus Waurick",

year = "2019",

month = jun,

day = "30",

doi = "10.1007/978-3-030-20016-9_12",

language = "English",

isbn = "9783030200152",

volume = "287",

pages = "285--307",

editor = "Saber Elaydi and Christian P{\"o}tzsche and Sasu, {Adina Lumini{\c t}a}",

booktitle = "Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 23, 2017",

publisher = "Springer New York",

address = "United States",

note = "23rd International Conference on Difference Equations and Applications, ICDEA 2017 ; Conference date: 24-07-2017 Through 28-07-2017",

}

Kitzing, K, Picard, R, Siegmund, S, Trostorff, S & Waurick, M 2019, A Hilbert space approach to difference equations. in S Elaydi, C Pötzsche & AL Sasu (eds), Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 23, 2017. vol. 287, Springer New York, pp. 285-307, 23rd International Conference on Difference Equations and Applications, ICDEA 2017, Timişoara, Romania, 24/07/17. https://doi.org/10.1007/978-3-030-20016-9_12

A Hilbert space approach to difference equations. / Kitzing, Konrad; Picard, Rainer; Siegmund, Stefan et al.
Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 23, 2017. ed. / Saber Elaydi; Christian Pötzsche; Adina Luminiţa Sasu. Vol. 287 Springer New York, 2019. p. 285-307.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - A Hilbert space approach to difference equations

AU - Kitzing, Konrad

AU - Picard, Rainer

AU - Siegmund, Stefan

AU - Trostorff, Sascha

AU - Waurick, Marcus

PY - 2019/6/30

Y1 - 2019/6/30

N2 - We consider general difference equations un+1= F(u) n for n∈ Z on exponentially weighted ℓ2 spaces of two-sided Hilbert space-valued sequences u and discuss initial value problems. As an application of the Hilbert space approach, we characterize exponential stability of linear equations and prove a stable manifold theorem for causal nonlinear difference equations.

AB - We consider general difference equations un+1= F(u) n for n∈ Z on exponentially weighted ℓ2 spaces of two-sided Hilbert space-valued sequences u and discuss initial value problems. As an application of the Hilbert space approach, we characterize exponential stability of linear equations and prove a stable manifold theorem for causal nonlinear difference equations.

KW - causality

KW - exponential stability

KW - exponentially weighted spaces

KW - non-linear difference equations

KW - stable manifold theorem

KW - Z transform

UR - http://www.scopus.com/inward/record.url?scp=85069196975&partnerID=8YFLogxK

UR - https://arxiv.org/abs/1807.05824

U2 - 10.1007/978-3-030-20016-9_12

DO - 10.1007/978-3-030-20016-9_12

M3 - Conference contribution book

AN - SCOPUS:85069196975

SN - 9783030200152

VL - 287

SP - 285

EP - 307

BT - Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 23, 2017

A2 - Elaydi, Saber

A2 - Pötzsche, Christian

A2 - Sasu, Adina Luminiţa

PB - Springer New York

T2 - 23rd International Conference on Difference Equations and Applications, ICDEA 2017

Y2 - 24 July 2017 through 28 July 2017

ER -

A Hilbert space approach to difference equations

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