Estimates of the Root Functions of a One-Dimensional Schrödinger Operator with a Strong Boundary Singularity
For any operator defined by the differential operation Lu = − u ″ + q ( x ) u on the interval G = (0, 1) with complex-valued potential q ( x ) locally integrable on G and satisfying the inequalities ∫ x 1 x 2 ζ | ( q ( ζ ) ) | d ζ ≤ l n ( x 1 / x 2 ) and ∫ x 1 x 2 ζ | ( q ( 1 − ζ ) ) | d ζ ≤ γ l n (...
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| Veröffentlicht in: | Differential equations 2018-05, Vol.54 (5), p.567-577 |
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| container_title | Differential equations |
| container_volume | 54 |
| creator | Borodinova, D. Yu Kritskov, L. V. |
| description | For any operator defined by the differential operation
Lu
= −
u
″ +
q
(
x
)
u
on the interval
G
= (0, 1) with complex-valued potential
q
(
x
) locally integrable on G and satisfying the inequalities
∫
x
1
x
2
ζ
|
(
q
(
ζ
)
)
|
d
ζ
≤
l
n
(
x
1
/
x
2
)
and
∫
x
1
x
2
ζ
|
(
q
(
1
−
ζ
)
)
|
d
ζ
≤
γ
l
n
(
x
1
/
x
2
)
with some constant γ for all sufficiently small 0 <
x
1
<
x
2
, we estimate the norms of root functions in the Lebesgue spaces
L
p
(
G
), 1 ≤
p
< ∞. We show that for sufficiently small γ these norms satisfy the same estimates asymptotic in the spectral parameter as in the unperturbed case. |
| doi_str_mv | 10.1134/S0012266118050014 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_proqu</sourceid><recordid>TN_cdi_proquest_journals_2052883656</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A720196887</galeid><sourcerecordid>A720196887</sourcerecordid><originalsourceid>FETCH-LOGICAL-c307t-2aed600f768669e3b4836ec87b4a405e510946df20d7d2eea80dee32d3ec7fda3</originalsourceid><addsrcrecordid>eNp1kc9KAzEQxoMoWKsP4C3geXWS7GbTY_0vCAWr5yVuZtuUNqlJFumL-QK-mKkVPIjMYYZvvt8wzBByyuCcMVFeTAEY51IypqDKdblHBkyCKgQosU8G23ax7R-SoxgXADCqWTUgq5uY7EonjNR3NM2RPnmf6G3v2mS9-1Y1nTgsru0KXcyaXtJpOw-fH8a6GQY6WWPQyQf6btM8m6cpeDejl753RocNnWZbv9TBps0xOej0MuLJTx6Sl9ub56v74nFy93A1fixaAXUquEYjAbpaKilHKF5LJSS2qn4tdQkVVgxGpTQdB1MbjqgVGETBjcC27owWQ3K2m7sO_q3HmJqF70PePDYcKq7yuEpm1_nONdNLbKzrfAq6zWFwZVvvsLNZH9cc2EgqVWeA7YA2-BgDds065OOFTcOg2b6h-fOGzPAdE7N3e6_fVf6HvgDcCIp2</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2052883656</pqid></control><display><type>article</type><title>Estimates of the Root Functions of a One-Dimensional Schrödinger Operator with a Strong Boundary Singularity</title><source>SpringerLink Journals - AutoHoldings</source><creator>Borodinova, D. Yu ; Kritskov, L. V.</creator><creatorcontrib>Borodinova, D. Yu ; Kritskov, L. V.</creatorcontrib><description>For any operator defined by the differential operation
Lu
= −
u
″ +
q
(
x
)
u
on the interval
G
= (0, 1) with complex-valued potential
q
(
x
) locally integrable on G and satisfying the inequalities
∫
x
1
x
2
ζ
|
(
q
(
ζ
)
)
|
d
ζ
≤
l
n
(
x
1
/
x
2
)
and
∫
x
1
x
2
ζ
|
(
q
(
1
−
ζ
)
)
|
d
ζ
≤
γ
l
n
(
x
1
/
x
2
)
with some constant γ for all sufficiently small 0 <
x
1
<
x
2
, we estimate the norms of root functions in the Lebesgue spaces
L
p
(
G
), 1 ≤
p
< ∞. We show that for sufficiently small γ these norms satisfy the same estimates asymptotic in the spectral parameter as in the unperturbed case.</description><identifier>ISSN: 0012-2661</identifier><identifier>EISSN: 1608-3083</identifier><identifier>DOI: 10.1134/S0012266118050014</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Asymptotic methods ; Difference and Functional Equations ; Differential equations ; Estimates ; Mathematics ; Mathematics and Statistics ; Norms ; Operators (mathematics) ; Ordinary Differential Equations ; Parameter estimation ; Partial Differential Equations</subject><ispartof>Differential equations, 2018-05, Vol.54 (5), p.567-577</ispartof><rights>Pleiades Publishing, Ltd. 2018</rights><rights>COPYRIGHT 2018 Springer</rights><rights>Differential Equations is a copyright of Springer, (2018). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c307t-2aed600f768669e3b4836ec87b4a405e510946df20d7d2eea80dee32d3ec7fda3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0012266118050014$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0012266118050014$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Borodinova, D. Yu</creatorcontrib><creatorcontrib>Kritskov, L. V.</creatorcontrib><title>Estimates of the Root Functions of a One-Dimensional Schrödinger Operator with a Strong Boundary Singularity</title><title>Differential equations</title><addtitle>Diff Equat</addtitle><description>For any operator defined by the differential operation
Lu
= −
u
″ +
q
(
x
)
u
on the interval
G
= (0, 1) with complex-valued potential
q
(
x
) locally integrable on G and satisfying the inequalities
∫
x
1
x
2
ζ
|
(
q
(
ζ
)
)
|
d
ζ
≤
l
n
(
x
1
/
x
2
)
and
∫
x
1
x
2
ζ
|
(
q
(
1
−
ζ
)
)
|
d
ζ
≤
γ
l
n
(
x
1
/
x
2
)
with some constant γ for all sufficiently small 0 <
x
1
<
x
2
, we estimate the norms of root functions in the Lebesgue spaces
L
p
(
G
), 1 ≤
p
< ∞. We show that for sufficiently small γ these norms satisfy the same estimates asymptotic in the spectral parameter as in the unperturbed case.</description><subject>Asymptotic methods</subject><subject>Difference and Functional Equations</subject><subject>Differential equations</subject><subject>Estimates</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Norms</subject><subject>Operators (mathematics)</subject><subject>Ordinary Differential Equations</subject><subject>Parameter estimation</subject><subject>Partial Differential Equations</subject><issn>0012-2661</issn><issn>1608-3083</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kc9KAzEQxoMoWKsP4C3geXWS7GbTY_0vCAWr5yVuZtuUNqlJFumL-QK-mKkVPIjMYYZvvt8wzBByyuCcMVFeTAEY51IypqDKdblHBkyCKgQosU8G23ax7R-SoxgXADCqWTUgq5uY7EonjNR3NM2RPnmf6G3v2mS9-1Y1nTgsru0KXcyaXtJpOw-fH8a6GQY6WWPQyQf6btM8m6cpeDejl753RocNnWZbv9TBps0xOej0MuLJTx6Sl9ub56v74nFy93A1fixaAXUquEYjAbpaKilHKF5LJSS2qn4tdQkVVgxGpTQdB1MbjqgVGETBjcC27owWQ3K2m7sO_q3HmJqF70PePDYcKq7yuEpm1_nONdNLbKzrfAq6zWFwZVvvsLNZH9cc2EgqVWeA7YA2-BgDds065OOFTcOg2b6h-fOGzPAdE7N3e6_fVf6HvgDcCIp2</recordid><startdate>20180501</startdate><enddate>20180501</enddate><creator>Borodinova, D. Yu</creator><creator>Kritskov, L. V.</creator><general>Pleiades Publishing</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>04Q</scope><scope>04W</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PADUT</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>PYYUZ</scope><scope>Q9U</scope></search><sort><creationdate>20180501</creationdate><title>Estimates of the Root Functions of a One-Dimensional Schrödinger Operator with a Strong Boundary Singularity</title><author>Borodinova, D. Yu ; Kritskov, L. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c307t-2aed600f768669e3b4836ec87b4a405e510946df20d7d2eea80dee32d3ec7fda3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Asymptotic methods</topic><topic>Difference and Functional Equations</topic><topic>Differential equations</topic><topic>Estimates</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Norms</topic><topic>Operators (mathematics)</topic><topic>Ordinary Differential Equations</topic><topic>Parameter estimation</topic><topic>Partial Differential Equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Borodinova, D. Yu</creatorcontrib><creatorcontrib>Kritskov, L. V.</creatorcontrib><collection>CrossRef</collection><collection>India Database</collection><collection>India Database: Science & Technology</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Research Library</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Research Library China</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><jtitle>Differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Borodinova, D. Yu</au><au>Kritskov, L. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Estimates of the Root Functions of a One-Dimensional Schrödinger Operator with a Strong Boundary Singularity</atitle><jtitle>Differential equations</jtitle><stitle>Diff Equat</stitle><date>2018-05-01</date><risdate>2018</risdate><volume>54</volume><issue>5</issue><spage>567</spage><epage>577</epage><pages>567-577</pages><issn>0012-2661</issn><eissn>1608-3083</eissn><abstract>For any operator defined by the differential operation
Lu
= −
u
″ +
q
(
x
)
u
on the interval
G
= (0, 1) with complex-valued potential
q
(
x
) locally integrable on G and satisfying the inequalities
∫
x
1
x
2
ζ
|
(
q
(
ζ
)
)
|
d
ζ
≤
l
n
(
x
1
/
x
2
)
and
∫
x
1
x
2
ζ
|
(
q
(
1
−
ζ
)
)
|
d
ζ
≤
γ
l
n
(
x
1
/
x
2
)
with some constant γ for all sufficiently small 0 <
x
1
<
x
2
, we estimate the norms of root functions in the Lebesgue spaces
L
p
(
G
), 1 ≤
p
< ∞. We show that for sufficiently small γ these norms satisfy the same estimates asymptotic in the spectral parameter as in the unperturbed case.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0012266118050014</doi><tpages>11</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0012-2661 |
| ispartof | Differential equations, 2018-05, Vol.54 (5), p.567-577 |
| issn | 0012-2661 1608-3083 |
| language | eng |
| recordid | cdi_proquest_journals_2052883656 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Asymptotic methods Difference and Functional Equations Differential equations Estimates Mathematics Mathematics and Statistics Norms Operators (mathematics) Ordinary Differential Equations Parameter estimation Partial Differential Equations |
| title | Estimates of the Root Functions of a One-Dimensional Schrödinger Operator with a Strong Boundary Singularity |
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