Open AccessOn some pseudo-differential equations and transmutation operators
Author(s) -
Vladimir Vasilyev
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1479/1/012009
Subject(s) - mathematics , sobolev space , differential equation , boundary value problem , mathematical analysis , nuclear transmutation , differential operator , elliptic operator , pure mathematics , algebra over a field , physics , neutron , quantum mechanics
We describe some operators for solving model elliptic pseudo-differential equations in special canonical domains. It helps us to write a general solution of corresponding pseudo-differential equation in an explicit form. Moreover, knowing a general solution we can choose additional (possibly boundary) conditions to determine uniquely the solution. All considerations we give in Sobolev–Slobodetskii spaces.