Strongly P-Positive Operators and Explicit Representations of the Solutions of Initial Value Problems for Second-Order Differential Equations in Banach Space

The initial value problems for two second-order differential equations with an unbounded operator coefficient A in a Banach space are considered. Using a linear fractional transform (the Cayley transform) of the operator A we give explicit formulas for the solution of these problems if the spectrum...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 1999-08, Vol.236 (2), p.327-349
Main Author: Gavrilyuk, Ivan P.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematics
Operator theory
Ordinary differential equations
Sciences and techniques of general use
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c355t-345e8bf994b6b792a50aa701d13c43d6320112b8fd4ab9e7f049fd92811f18273
cites cdi_FETCH-LOGICAL-c355t-345e8bf994b6b792a50aa701d13c43d6320112b8fd4ab9e7f049fd92811f18273
container_end_page 349
container_issue 2
container_start_page 327
container_title Journal of mathematical analysis and applications
container_volume 236
creator Gavrilyuk, Ivan P.
description The initial value problems for two second-order differential equations with an unbounded operator coefficient A in a Banach space are considered. Using a linear fractional transform (the Cayley transform) of the operator A we give explicit formulas for the solution of these problems if the spectrum of A is situated inside of a parabola. These formulas also provide the algorithmic representations of the operator cosine-function and of the operator Bessel-function with the generator A being a basis for approximate solutions for which error estimates are given. One of the important properties of our approach is the following: the accuracy of the approximate solutions depends automatically on the regularity of the initial data.
doi_str_mv 10.1006/jmaa.1999.6430
format article
fullrecord <record><control><sourceid>elsevier_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1006_jmaa_1999_6430</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0022247X99964302</els_id><sourcerecordid>S0022247X99964302</sourcerecordid><originalsourceid>FETCH-LOGICAL-c355t-345e8bf994b6b792a50aa701d13c43d6320112b8fd4ab9e7f049fd92811f18273</originalsourceid><addsrcrecordid>eNp1kE1rGzEQhkVpIG7aa8469LqOtNovHdvUSQwBmzoJvS2z0qiWWUtbSTbJj8l_7S4O7SknwfC-z2geQi45m3PGqqvdHmDOpZTzqhDsA5lxJquMNVx8JDPG8jzLi_rXOfkU444xzsuaz8jrJgXvfvcvdJ2tfbTJHpGuBgyQfIgUnKaL56G3yib6E4eAEV2CZL2L1Buatkg3vj_8GyzdiICePkF_QLoOvutxH6nxgW5QeaezVdAY6A9rDIaRNYUXfw5vSOvod3CgtnQzgMLP5MxAH_HL23tBHm8WD9d32f3qdnn97T5ToixTJooSm85IWXRVV8scSgZQM665UIXQlcjHc_OuMbqATmJtWCGNlnnDueFNXosLMj9xVfAxBjTtEOwewkvLWTvJbSe57SS3neSOha-nwgBRQW8COGXj_5bkdVmLMdacYjh-_mgxtFFZdAq1DahSq719b8Nf9yCQQg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Strongly P-Positive Operators and Explicit Representations of the Solutions of Initial Value Problems for Second-Order Differential Equations in Banach Space</title><source>ScienceDirect Journals</source><creator>Gavrilyuk, Ivan P.</creator><creatorcontrib>Gavrilyuk, Ivan P.</creatorcontrib><description>The initial value problems for two second-order differential equations with an unbounded operator coefficient A in a Banach space are considered. Using a linear fractional transform (the Cayley transform) of the operator A we give explicit formulas for the solution of these problems if the spectrum of A is situated inside of a parabola. These formulas also provide the algorithmic representations of the operator cosine-function and of the operator Bessel-function with the generator A being a basis for approximate solutions for which error estimates are given. One of the important properties of our approach is the following: the accuracy of the approximate solutions depends automatically on the regularity of the initial data.</description><identifier>ISSN: 0022-247X</identifier><identifier>EISSN: 1096-0813</identifier><identifier>DOI: 10.1006/jmaa.1999.6430</identifier><identifier>CODEN: JMANAK</identifier><language>eng</language><publisher>San Diego, CA: Elsevier Inc</publisher><subject>Exact sciences and technology ; Mathematical analysis ; Mathematics ; Operator theory ; Ordinary differential equations ; Sciences and techniques of general use</subject><ispartof>Journal of mathematical analysis and applications, 1999-08, Vol.236 (2), p.327-349</ispartof><rights>1999 Academic Press</rights><rights>1999 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-345e8bf994b6b792a50aa701d13c43d6320112b8fd4ab9e7f049fd92811f18273</citedby><cites>FETCH-LOGICAL-c355t-345e8bf994b6b792a50aa701d13c43d6320112b8fd4ab9e7f049fd92811f18273</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&amp;idt=1917573$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Gavrilyuk, Ivan P.</creatorcontrib><title>Strongly P-Positive Operators and Explicit Representations of the Solutions of Initial Value Problems for Second-Order Differential Equations in Banach Space</title><title>Journal of mathematical analysis and applications</title><description>The initial value problems for two second-order differential equations with an unbounded operator coefficient A in a Banach space are considered. Using a linear fractional transform (the Cayley transform) of the operator A we give explicit formulas for the solution of these problems if the spectrum of A is situated inside of a parabola. These formulas also provide the algorithmic representations of the operator cosine-function and of the operator Bessel-function with the generator A being a basis for approximate solutions for which error estimates are given. One of the important properties of our approach is the following: the accuracy of the approximate solutions depends automatically on the regularity of the initial data.</description><subject>Exact sciences and technology</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Operator theory</subject><subject>Ordinary differential equations</subject><subject>Sciences and techniques of general use</subject><issn>0022-247X</issn><issn>1096-0813</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><recordid>eNp1kE1rGzEQhkVpIG7aa8469LqOtNovHdvUSQwBmzoJvS2z0qiWWUtbSTbJj8l_7S4O7SknwfC-z2geQi45m3PGqqvdHmDOpZTzqhDsA5lxJquMNVx8JDPG8jzLi_rXOfkU444xzsuaz8jrJgXvfvcvdJ2tfbTJHpGuBgyQfIgUnKaL56G3yib6E4eAEV2CZL2L1Buatkg3vj_8GyzdiICePkF_QLoOvutxH6nxgW5QeaezVdAY6A9rDIaRNYUXfw5vSOvod3CgtnQzgMLP5MxAH_HL23tBHm8WD9d32f3qdnn97T5ToixTJooSm85IWXRVV8scSgZQM665UIXQlcjHc_OuMbqATmJtWCGNlnnDueFNXosLMj9xVfAxBjTtEOwewkvLWTvJbSe57SS3neSOha-nwgBRQW8COGXj_5bkdVmLMdacYjh-_mgxtFFZdAq1DahSq719b8Nf9yCQQg</recordid><startdate>19990815</startdate><enddate>19990815</enddate><creator>Gavrilyuk, Ivan P.</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19990815</creationdate><title>Strongly P-Positive Operators and Explicit Representations of the Solutions of Initial Value Problems for Second-Order Differential Equations in Banach Space</title><author>Gavrilyuk, Ivan P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-345e8bf994b6b792a50aa701d13c43d6320112b8fd4ab9e7f049fd92811f18273</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><topic>Exact sciences and technology</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Operator theory</topic><topic>Ordinary differential equations</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gavrilyuk, Ivan P.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>Journal of mathematical analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gavrilyuk, Ivan P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Strongly P-Positive Operators and Explicit Representations of the Solutions of Initial Value Problems for Second-Order Differential Equations in Banach Space</atitle><jtitle>Journal of mathematical analysis and applications</jtitle><date>1999-08-15</date><risdate>1999</risdate><volume>236</volume><issue>2</issue><spage>327</spage><epage>349</epage><pages>327-349</pages><issn>0022-247X</issn><eissn>1096-0813</eissn><coden>JMANAK</coden><abstract>The initial value problems for two second-order differential equations with an unbounded operator coefficient A in a Banach space are considered. Using a linear fractional transform (the Cayley transform) of the operator A we give explicit formulas for the solution of these problems if the spectrum of A is situated inside of a parabola. These formulas also provide the algorithmic representations of the operator cosine-function and of the operator Bessel-function with the generator A being a basis for approximate solutions for which error estimates are given. One of the important properties of our approach is the following: the accuracy of the approximate solutions depends automatically on the regularity of the initial data.</abstract><cop>San Diego, CA</cop><pub>Elsevier Inc</pub><doi>10.1006/jmaa.1999.6430</doi><tpages>23</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0022-247X
ispartof Journal of mathematical analysis and applications, 1999-08, Vol.236 (2), p.327-349
issn 0022-247X
1096-0813
language eng
recordid cdi_crossref_primary_10_1006_jmaa_1999_6430
source ScienceDirect Journals
subjects Exact sciences and technology
Mathematical analysis
Mathematics
Operator theory
Ordinary differential equations
Sciences and techniques of general use
title Strongly P-Positive Operators and Explicit Representations of the Solutions of Initial Value Problems for Second-Order Differential Equations in Banach Space
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-23T16%3A58%3A57IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-elsevier_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Strongly%20P-Positive%20Operators%20and%20Explicit%20Representations%20of%20the%20Solutions%20of%20Initial%20Value%20Problems%20for%20Second-Order%20Differential%20Equations%20in%20Banach%20Space&rft.jtitle=Journal%20of%20mathematical%20analysis%20and%20applications&rft.au=Gavrilyuk,%20Ivan%20P.&rft.date=1999-08-15&rft.volume=236&rft.issue=2&rft.spage=327&rft.epage=349&rft.pages=327-349&rft.issn=0022-247X&rft.eissn=1096-0813&rft.coden=JMANAK&rft_id=info:doi/10.1006/jmaa.1999.6430&rft_dat=%3Celsevier_cross%3ES0022247X99964302%3C/elsevier_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c355t-345e8bf994b6b792a50aa701d13c43d6320112b8fd4ab9e7f049fd92811f18273%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true