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B-evolusies en die laplace transformasie
Dissertation (MSc (Applied Mathematics))--University of Pretoria, 1986.
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| Format: | Thesis |
| Language: | Afr |
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University of Pretoria
2024
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| _version_ | 1867613640989868032 |
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| access_status_str | Open Access |
| author2 | Sauer, N. (Niko) |
| author_browse | Sauer, N. (Niko) |
| author_facet | Sauer, N. (Niko) |
| collection | Thesis |
| dc_rights_str_mv | © 2024 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc (Applied Mathematics))--University of Pretoria, 1986. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/99596 |
| institution | University of Pretoria (South Africa) |
| language | Afr |
| last_indexed | 2026-06-10T12:39:22.254Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/99596 B-evolusies en die laplace transformasie Sauer, N. (Niko) Jooste Aletta Sophia B-evolusies Laplace transformasie UCTD Dissertation (MSc (Applied Mathematics))--University of Pretoria, 1986. If Bis a linear operator with domain DCB) contained in a Banach space X and range in a Banach space Y, the family {S(t):t>O} of bounded, linear operators defined on Y is called a B-evolution if S(t)CYJ c D(B) and SCt+s) = S<t>BS(s) for all positive t ands. Associated with SCt> is the semi-group {E(t):t>O} of linear operators in Y, defined by ECt) = BS(t). In this dissertation the properties of a-evolutions are studied. Certain assumptions are made with respect to S(t) and E Ct>. The infinitesimal operator Ao of S(t) is de= fined and it is shown that restrictions of Ao and the operator B form a closable pair. The closure of this pair is denoted by <a,e> and it is shown that the operator ~e - a, with Re~>O, maps PC~)[YJ onto Y and where P<~> is the Laplace transform of S<t>. The closed pair <a,e> will determine the B-evolution uniquely only if S<t> is strongly continuous for t>O. The initial states y for which u<t> = S<t>y solves tha Cauchy problem are also determined. DtCBu(t)J = Aou(t) Bu(t>lt-o = y. The link between S<t> and E<t> is studied. An unbounded operator C, that links the B-evolution S(t) and its associated semi-group E<t>, is constructed such that S(t) = CE<t>. Finally, the concept of a family of operators which is in empathy with a semi-group is introduced. Such families are studied, and conditions determined under which they are B-evolutions. Mathematics and Applied Mathematics MSc (Applied Mathematics) 2024-11-27T09:16:24Z 2024-11-27T09:16:24Z 22/01/13 1986 Dissertation http://hdl.handle.net/2263/99596 Afr © 2024 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | B-evolusies Laplace transformasie UCTD B-evolusies en die laplace transformasie |
| title | B-evolusies en die laplace transformasie |
| title_full | B-evolusies en die laplace transformasie |
| title_fullStr | B-evolusies en die laplace transformasie |
| title_full_unstemmed | B-evolusies en die laplace transformasie |
| title_short | B-evolusies en die laplace transformasie |
| title_sort | b evolusies en die laplace transformasie |
| topic | B-evolusies Laplace transformasie UCTD |
| url | http://hdl.handle.net/2263/99596 |