Fractional Laplace Operator and Meijer G-function
We significantly expand the number of functions whose image under the fractional Laplace operator can be computed explicitly. In particular, we show that the fractional Laplace operator maps Meijer G-functions of | x | 2 , or generalized hypergeometric functions of - | x | 2 , multiplied by a solid...
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| Veröffentlicht in: | Constructive approximation 2017-06, Vol.45 (3), p.427-448 |
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| container_title | Constructive approximation |
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| creator | Dyda, Bartłomiej Kuznetsov, Alexey Kwaśnicki, Mateusz |
| description | We significantly expand the number of functions whose image under the fractional Laplace operator can be computed explicitly. In particular, we show that the fractional Laplace operator maps Meijer G-functions of
|
x
|
2
, or generalized hypergeometric functions of
-
|
x
|
2
, multiplied by a solid harmonic polynomial, into the same class of functions. As one important application of this result, we produce a complete system of eigenfunctions of the operator
(
1
-
|
x
|
2
)
+
α
/
2
(
-
Δ
)
α
/
2
with the Dirichlet boundary conditions outside of the unit ball. The latter result will be used to estimate the eigenvalues of the fractional Laplace operator in the unit ball in a companion paper (Dyda et al., Eigenvalues of the fractional Laplace operator in the unit ball,
2015
,
arXiv:1509.08533
). |
| doi_str_mv | 10.1007/s00365-016-9336-4 |
| format | Article |
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|
x
|
2
, or generalized hypergeometric functions of
-
|
x
|
2
, multiplied by a solid harmonic polynomial, into the same class of functions. As one important application of this result, we produce a complete system of eigenfunctions of the operator
(
1
-
|
x
|
2
)
+
α
/
2
(
-
Δ
)
α
/
2
with the Dirichlet boundary conditions outside of the unit ball. The latter result will be used to estimate the eigenvalues of the fractional Laplace operator in the unit ball in a companion paper (Dyda et al., Eigenvalues of the fractional Laplace operator in the unit ball,
2015
,
arXiv:1509.08533
).</description><identifier>ISSN: 0176-4276</identifier><identifier>EISSN: 1432-0940</identifier><identifier>DOI: 10.1007/s00365-016-9336-4</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Analysis ; Hypergeometric functions ; Mathematics ; Mathematics and Statistics ; Numerical Analysis</subject><ispartof>Constructive approximation, 2017-06, Vol.45 (3), p.427-448</ispartof><rights>Springer Science+Business Media New York 2016</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-b1f6ff980059a72d3335dcf6b3f32b97f375361c5980eb6c8b741c18efb54ff43</citedby><cites>FETCH-LOGICAL-c316t-b1f6ff980059a72d3335dcf6b3f32b97f375361c5980eb6c8b741c18efb54ff43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00365-016-9336-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00365-016-9336-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Dyda, Bartłomiej</creatorcontrib><creatorcontrib>Kuznetsov, Alexey</creatorcontrib><creatorcontrib>Kwaśnicki, Mateusz</creatorcontrib><title>Fractional Laplace Operator and Meijer G-function</title><title>Constructive approximation</title><addtitle>Constr Approx</addtitle><description>We significantly expand the number of functions whose image under the fractional Laplace operator can be computed explicitly. In particular, we show that the fractional Laplace operator maps Meijer G-functions of
|
x
|
2
, or generalized hypergeometric functions of
-
|
x
|
2
, multiplied by a solid harmonic polynomial, into the same class of functions. As one important application of this result, we produce a complete system of eigenfunctions of the operator
(
1
-
|
x
|
2
)
+
α
/
2
(
-
Δ
)
α
/
2
with the Dirichlet boundary conditions outside of the unit ball. The latter result will be used to estimate the eigenvalues of the fractional Laplace operator in the unit ball in a companion paper (Dyda et al., Eigenvalues of the fractional Laplace operator in the unit ball,
2015
,
arXiv:1509.08533
).</description><subject>Analysis</subject><subject>Hypergeometric functions</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical Analysis</subject><issn>0176-4276</issn><issn>1432-0940</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kDFPwzAQhS0EEqXwA9giMRvucrEdj6iiLVJQF5gtx7VRopIEOx3496SEgYXppKfvPZ0-xm4R7hFAPSQAkoIDSq6JJC_O2AILyjnoAs7ZAlBNYa7kJbtKqQVAUZJaMFxH68am7-whq-xwsM5nu8FHO_Yxs90-e_FN62O24eHY_YDX7CLYQ_I3v3fJ3tZPr6str3ab59VjxR2hHHmNQYagSwChrcr3RCT2LsiaAuW1VoGUIIlOTIivpStrVaDD0odaFCEUtGR38-4Q-8-jT6Np-2Oc_kwGS52T0kqIicKZcrFPKfpghth82PhlEMzJjJnNmMmMOZkxp-V87qSJ7d59_LP8b-kb2XFkaQ</recordid><startdate>20170601</startdate><enddate>20170601</enddate><creator>Dyda, Bartłomiej</creator><creator>Kuznetsov, Alexey</creator><creator>Kwaśnicki, Mateusz</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170601</creationdate><title>Fractional Laplace Operator and Meijer G-function</title><author>Dyda, Bartłomiej ; Kuznetsov, Alexey ; Kwaśnicki, Mateusz</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-b1f6ff980059a72d3335dcf6b3f32b97f375361c5980eb6c8b741c18efb54ff43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Analysis</topic><topic>Hypergeometric functions</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical Analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dyda, Bartłomiej</creatorcontrib><creatorcontrib>Kuznetsov, Alexey</creatorcontrib><creatorcontrib>Kwaśnicki, Mateusz</creatorcontrib><collection>CrossRef</collection><jtitle>Constructive approximation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dyda, Bartłomiej</au><au>Kuznetsov, Alexey</au><au>Kwaśnicki, Mateusz</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fractional Laplace Operator and Meijer G-function</atitle><jtitle>Constructive approximation</jtitle><stitle>Constr Approx</stitle><date>2017-06-01</date><risdate>2017</risdate><volume>45</volume><issue>3</issue><spage>427</spage><epage>448</epage><pages>427-448</pages><issn>0176-4276</issn><eissn>1432-0940</eissn><abstract>We significantly expand the number of functions whose image under the fractional Laplace operator can be computed explicitly. In particular, we show that the fractional Laplace operator maps Meijer G-functions of
|
x
|
2
, or generalized hypergeometric functions of
-
|
x
|
2
, multiplied by a solid harmonic polynomial, into the same class of functions. As one important application of this result, we produce a complete system of eigenfunctions of the operator
(
1
-
|
x
|
2
)
+
α
/
2
(
-
Δ
)
α
/
2
with the Dirichlet boundary conditions outside of the unit ball. The latter result will be used to estimate the eigenvalues of the fractional Laplace operator in the unit ball in a companion paper (Dyda et al., Eigenvalues of the fractional Laplace operator in the unit ball,
2015
,
arXiv:1509.08533
).</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00365-016-9336-4</doi><tpages>22</tpages></addata></record> |
| fulltext | fulltext |
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| ispartof | Constructive approximation, 2017-06, Vol.45 (3), p.427-448 |
| issn | 0176-4276 1432-0940 |
| language | eng |
| recordid | cdi_proquest_journals_1892379755 |
| source | Springer Nature |
| subjects | Analysis Hypergeometric functions Mathematics Mathematics and Statistics Numerical Analysis |
| title | Fractional Laplace Operator and Meijer G-function |
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