The abstract Cauchy problem in locally convex spaces

Karsten Kruse

doi:10.1007/s13398-022-01295-5

The abstract Cauchy problem in locally convex spaces

Karsten Kruse^*

^*Corresponding author for this work

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

11 Downloads (Pure)

Abstract

We derive necessary and sufficient criteria for the uniqueness and existence of solutions of the abstract Cauchy problem in locally convex Hausdorff spaces. Our approach is based on a suitable notion of an asymptotic Laplace transform and extends results of Langenbruch beyond the class of Fréchet spaces.

Original language	English
Article number	155
Journal	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume	116
Issue number	4
DOIs	https://doi.org/10.1007/s13398-022-01295-5
Publication status	Published - Oct 2022
Externally published	Yes

Keywords

Abstract Cauchy problem
Asymptotic Laplace transform
Asymptotic resolvent
Hyperfunction

Access to Document

10.1007/s13398-022-01295-5Licence: CC BY

s13398-022-01295-5Final published version, 555 KBLicence: CC BY

Cite this

@article{1577acc6598f42408d85f662d4f20e1b,

title = "The abstract Cauchy problem in locally convex spaces",

abstract = "We derive necessary and sufficient criteria for the uniqueness and existence of solutions of the abstract Cauchy problem in locally convex Hausdorff spaces. Our approach is based on a suitable notion of an asymptotic Laplace transform and extends results of Langenbruch beyond the class of Fr{\'e}chet spaces.",

keywords = "Abstract Cauchy problem, Asymptotic Laplace transform, Asymptotic resolvent, Hyperfunction",

author = "Karsten Kruse",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2022",

month = oct,

doi = "10.1007/s13398-022-01295-5",

language = "English",

volume = "116",

journal = "Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas",

issn = "1578-7303",

publisher = "Springer",

number = "4",

}

TY - JOUR

T1 - The abstract Cauchy problem in locally convex spaces

AU - Kruse, Karsten

PY - 2022/10

Y1 - 2022/10

N2 - We derive necessary and sufficient criteria for the uniqueness and existence of solutions of the abstract Cauchy problem in locally convex Hausdorff spaces. Our approach is based on a suitable notion of an asymptotic Laplace transform and extends results of Langenbruch beyond the class of Fréchet spaces.

AB - We derive necessary and sufficient criteria for the uniqueness and existence of solutions of the abstract Cauchy problem in locally convex Hausdorff spaces. Our approach is based on a suitable notion of an asymptotic Laplace transform and extends results of Langenbruch beyond the class of Fréchet spaces.

KW - Abstract Cauchy problem

KW - Asymptotic Laplace transform

KW - Asymptotic resolvent

KW - Hyperfunction

UR - https://www.scopus.com/pages/publications/85134594509

U2 - 10.1007/s13398-022-01295-5

DO - 10.1007/s13398-022-01295-5

M3 - Article

AN - SCOPUS:85134594509

SN - 1578-7303

VL - 116

JO - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

JF - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

IS - 4

M1 - 155

ER -

The abstract Cauchy problem in locally convex spaces

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this