On a transformation of integral equations
Let E = E ( a , b ) be some Banach space of measurable functions on ( a , b ), I be the identity operator, and let K ^ be a Fredholm-type regular integral operator acting on E and K ^ ± be its triangular parts. We consider the representation I − K ^ = ( I − K ^ − ) ( I − U ^ ) ( I − K ^ + ) , for so...
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| Veröffentlicht in: | Journal of contemporary mathematical analysis 2017-11, Vol.52 (6), p.288-294 |
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| container_title | Journal of contemporary mathematical analysis |
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| creator | Yengibaryan, B. N. Yengibaryan, N. B. |
| description | Let
E
=
E
(
a
,
b
) be some Banach space of measurable functions on (
a
,
b
),
I
be the identity operator, and let
K
^
be a Fredholm-type regular integral operator acting on
E
and
K
^
±
be its triangular parts. We consider the representation
I
−
K
^
=
(
I
−
K
^
−
)
(
I
−
U
^
)
(
I
−
K
^
+
)
, for some known classes of integral operators. In particular,we show that under certain conditions the operator
U
^
is positive and its spectral radius satisfies the condition
r
(
U
^
)
<
1
. Also, we give some possible applications of the representation. |
| doi_str_mv | 10.3103/S1068362317060048 |
| format | Article |
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E
=
E
(
a
,
b
) be some Banach space of measurable functions on (
a
,
b
),
I
be the identity operator, and let
K
^
be a Fredholm-type regular integral operator acting on
E
and
K
^
±
be its triangular parts. We consider the representation
I
−
K
^
=
(
I
−
K
^
−
)
(
I
−
U
^
)
(
I
−
K
^
+
)
, for some known classes of integral operators. In particular,we show that under certain conditions the operator
U
^
is positive and its spectral radius satisfies the condition
r
(
U
^
)
<
1
. Also, we give some possible applications of the representation.</description><identifier>ISSN: 1068-3623</identifier><identifier>EISSN: 1934-9416</identifier><identifier>DOI: 10.3103/S1068362317060048</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Banach spaces ; Integral Equations ; Mathematics ; Mathematics and Statistics ; Operators (mathematics) ; Representations</subject><ispartof>Journal of contemporary mathematical analysis, 2017-11, Vol.52 (6), p.288-294</ispartof><rights>Allerton Press, Inc. 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.3103/S1068362317060048$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.3103/S1068362317060048$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27906,27907,41470,42539,51301</link.rule.ids></links><search><creatorcontrib>Yengibaryan, B. N.</creatorcontrib><creatorcontrib>Yengibaryan, N. B.</creatorcontrib><title>On a transformation of integral equations</title><title>Journal of contemporary mathematical analysis</title><addtitle>J. Contemp. Mathemat. Anal</addtitle><description>Let
E
=
E
(
a
,
b
) be some Banach space of measurable functions on (
a
,
b
),
I
be the identity operator, and let
K
^
be a Fredholm-type regular integral operator acting on
E
and
K
^
±
be its triangular parts. We consider the representation
I
−
K
^
=
(
I
−
K
^
−
)
(
I
−
U
^
)
(
I
−
K
^
+
)
, for some known classes of integral operators. In particular,we show that under certain conditions the operator
U
^
is positive and its spectral radius satisfies the condition
r
(
U
^
)
<
1
. Also, we give some possible applications of the representation.</description><subject>Banach spaces</subject><subject>Integral Equations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Representations</subject><issn>1068-3623</issn><issn>1934-9416</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1UDtPwzAQthBIlMIPYIvExBC4ix-xR1Txkip1AGbLcewqVRu3djLw73EJAxJiuk9330P3EXKNcEcR6P0bgpBUVBRrEABMnpAZKspKxVCcZpzP5fF-Ti5S2gDwjNmM3K76whRDNH3yIe7M0IW-CL7o-sGto9kW7jB-L9MlOfNmm9zVz5yTj6fH98VLuVw9vy4elqWthBxKpxyVtuKcopUWraEgXJ3DhAHBuFBOKkYliKZtJMeWc9m6RnkGxtfoGzonN5PvPobD6NKgN2GMfY7UqLLu-BBmFk4sG0NK0Xm9j93OxE-NoI-N6D-NZE01aVLm9msXfzn_K_oCKPBgUg</recordid><startdate>20171101</startdate><enddate>20171101</enddate><creator>Yengibaryan, B. N.</creator><creator>Yengibaryan, N. B.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20171101</creationdate><title>On a transformation of integral equations</title><author>Yengibaryan, B. N. ; Yengibaryan, N. B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-e9e38c25531c8c1ca306e76236a064569e8943806bdb851d558deb9f40af71fb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Banach spaces</topic><topic>Integral Equations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><topic>Representations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yengibaryan, B. N.</creatorcontrib><creatorcontrib>Yengibaryan, N. B.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of contemporary mathematical analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yengibaryan, B. N.</au><au>Yengibaryan, N. B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On a transformation of integral equations</atitle><jtitle>Journal of contemporary mathematical analysis</jtitle><stitle>J. Contemp. Mathemat. Anal</stitle><date>2017-11-01</date><risdate>2017</risdate><volume>52</volume><issue>6</issue><spage>288</spage><epage>294</epage><pages>288-294</pages><issn>1068-3623</issn><eissn>1934-9416</eissn><abstract>Let
E
=
E
(
a
,
b
) be some Banach space of measurable functions on (
a
,
b
),
I
be the identity operator, and let
K
^
be a Fredholm-type regular integral operator acting on
E
and
K
^
±
be its triangular parts. We consider the representation
I
−
K
^
=
(
I
−
K
^
−
)
(
I
−
U
^
)
(
I
−
K
^
+
)
, for some known classes of integral operators. In particular,we show that under certain conditions the operator
U
^
is positive and its spectral radius satisfies the condition
r
(
U
^
)
<
1
. Also, we give some possible applications of the representation.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.3103/S1068362317060048</doi><tpages>7</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1068-3623 |
| ispartof | Journal of contemporary mathematical analysis, 2017-11, Vol.52 (6), p.288-294 |
| issn | 1068-3623 1934-9416 |
| language | eng |
| recordid | cdi_proquest_journals_1980694161 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Banach spaces Integral Equations Mathematics Mathematics and Statistics Operators (mathematics) Representations |
| title | On a transformation of integral equations |
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