Analiz Na Kvazimetricheskikh Prostranstvakh. Greshnov Aleksandr

ISBN: 9783847391180

Published: March 8th 2012

Paperback

232 pages


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Analiz Na Kvazimetricheskikh Prostranstvakh.  by  Greshnov Aleksandr

Analiz Na Kvazimetricheskikh Prostranstvakh. by Greshnov Aleksandr
March 8th 2012 | Paperback | PDF, EPUB, FB2, DjVu, talking book, mp3, RTF | 232 pages | ISBN: 9783847391180 | 8.64 Mb

Pod kvazimetrikoy obychno podrazumevaetsya neotritsatelnaya funktsiya d= d(u, v), opredelennaya na AxA, gde A nekotoroe mnozhestvo, takaya, chto dlya nee vypolnyayutsya metricheskie aksiomy tozhdestva, simmetrii i obobshchennoe neravenstvoMorePod kvazimetrikoy obychno podrazumevaetsya neotritsatelnaya funktsiya d= d(u, v), opredelennaya na AxA, gde A nekotoroe mnozhestvo, takaya, chto dlya nee vypolnyayutsya metricheskie aksiomy tozhdestva, simmetrii i obobshchennoe neravenstvo treugolnika. Para (A, d) nazyvaetsya kvazimetricheskim prostranstvom ili kvaziprostranstvom.

Izuchenie kvaziprostranstv motivirovano zadachami teorii subellipticheskikh uravneniy, singulyarnoy geometrii, i dr. Chastnym sluchaem kvaziprostranstv yavlyayutsya kvaziprostranstva s kvazimetrikami, ekvivalentnnymi metrikam Karno Karateodori. V rabote issledovana geometriya podobnykh kvaziprostranstv kak takovykh (metriki i kvazimetriki, gorizontalnye krivye, lokalnye approksimatsii modelnymi prostranstvami, razlichnye tipy podoblastey), a takzhe lokalnye svoystva sistem vektornykh poley, zadayushchikh takie struktury, i sootvetstvuyushchikh eksponentsialnykh otobrazheniy.

V tsentre vnimaniya nakhoditsya slozhnaya dlya analiza situatsiya struktur maloy gladkosti. Dokazany teoremy o sushchestvovanii odnorodnoy nilpotentnoy approksimatsii dlya bazisnykh vektornykh poley pri minimalnykh predpolozheniyakh na ikh gladkost, postroeny primery ravnomernykh i NTA oblastey v geometrii Karno Karateodori, i dr.



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