KO‘P O‘LCHAMLI BESSEL OPERATORLARIGA ASOSLANGAN LAPLAS–BESSEL DIFFERENSIAL OPERATORINING FORMAL O‘Z-O‘ZIGA QO‘SHMALIGI VA BIR JINSLILIK XOSSALARI HAQIDA
DOI:
https://doi.org/10.5281/zenodo.22852839Abstract
Mazkur maqolada ko‘p o‘lchamli Bessel differensial operatoriga asoslangan Laplas-Bessel operatori (Kipriyanov operatori, Δʙ) ko‘rib chiqiladi. Operatorning qat’iy ta’rifi, uning klassik Laplas operatori bilan bog‘liqligi, vaznli Lebeg fazolarida formal o‘z-o‘ziga qo‘shma (self-adjoint) ekanligi va bir jinslilik xossasi to‘liq isbotlari bilan keltiriladi. Shuningdek, operatorning umumlashgan siljish operatori bilan bog‘liqligi, fundamental yechimi hamda operator asosida qurilgan B-elliptik, B-parabolik va B-giperbolik tenglamalar sinflari haqida umumiy nazariy ma’lumot beriladi.Keywords
Laplas-Bessel operatori, Bessel differensial operatori, umumlashgan siljish operatori, vaznli Lebeg fazosi, B-elliptik tenglamalar, fundamental yechimReferences
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