Solution space characterisation of perturbed linear functional and integrodifferential Volterra convolution equations: Cesàro limits Article Swipe
John A. D. Appleby
,
Emmet Lawless
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2407.08416
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2407.08416
In this article we discuss the requirements needed in order to characterise the solution space of perturbed linear integro-differential Volterra convolution equations. We highlight in general how the pointwise behaviour of perturbation functions does not necessarily propagate through to the solution which the classical literature seems to suggest. To illustrate this general idea we show the Cesàro mean of the solution can converge even in cases when the Cesàro mean of the perturbation function diverges. Furthermore we provide a characterisation of when such convergence takes place and explicitly identify the limit in terms of the problem data. Additionally we prove how all results can also be applied to perturbed linear functional differential equations.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2407.08416
- https://arxiv.org/pdf/2407.08416
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4400611828
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https://openalex.org/W4400611828Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2407.08416Digital Object Identifier
- Title
-
Solution space characterisation of perturbed linear functional and integrodifferential Volterra convolution equations: Cesàro limitsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-07-11Full publication date if available
- Authors
-
John A. D. Appleby, Emmet LawlessList of authors in order
- Landing page
-
https://arxiv.org/abs/2407.08416Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2407.08416Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2407.08416Direct OA link when available
- Concepts
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Convolution (computer science), Volterra equations, Space (punctuation), Mathematics, Mathematical analysis, Applied mathematics, Volterra integral equation, Nonlinear system, Physics, Computer science, Integral equation, Quantum mechanics, Artificial neural network, Machine learning, Operating systemTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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