{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T06:59:38Z","timestamp":1774594778693,"version":"3.50.1"},"reference-count":0,"publisher":"Wiley","issue":"8","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>The pseudodifferential operator (p.d.o.) <jats:italic>A<\/jats:italic>(<jats:italic>x<\/jats:italic>, <jats:italic>D<\/jats:italic>), associated with the Bessel operator <jats:italic>d<\/jats:italic><jats:sup>2<\/jats:sup>\/<jats:italic>d<\/jats:italic><jats:italic>x<\/jats:italic><jats:sup>2<\/jats:sup> + (1 \u2212 4<jats:italic>\u03bc<\/jats:italic><jats:sup>2<\/jats:sup>)\/4<jats:italic>x<\/jats:italic><jats:sup>2<\/jats:sup>, is defined. Symbol class  is introduced. It is shown that the p.d.o. associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian space <jats:italic>H<\/jats:italic><jats:sub><jats:italic>\u03bc<\/jats:italic><\/jats:sub> into itself. An integral representation of p.d.o. is obtained. Using Hankel convolution \u2010norm continuity of the p.d.o. is proved.<\/jats:p>","DOI":"10.1155\/s0161171204212388","type":"journal-article","created":{"date-parts":[[2004,2,18]],"date-time":"2004-02-18T13:25:48Z","timestamp":1077110748000},"page":"407-419","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The pseudodifferential operator <i>A<\/i>(<i>x<\/i>, <i>D<\/i>)"],"prefix":"10.1155","volume":"2004","author":[{"given":"R. S.","family":"Pathak","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"Pathak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2004,2,18]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/848506.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171204212388","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T19:59:11Z","timestamp":1723060751000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171204212388"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":0,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1155\/S0161171204212388"],"URL":"https:\/\/doi.org\/10.1155\/s0161171204212388","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1]]},"assertion":[{"value":"2002-12-16","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2004-02-18","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}