Open AccessOn the resolvent existence and the separability of a hyperbolic operator with fast growing coefficients in L2(R2)
Author(s) -
М.B. Muratbekov,
Yerik Bayandiyev
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2103707m
Subject(s) - mathematics , resolvent , differential operator , domain (mathematical analysis) , smoothness , mathematical analysis , infinity , closure (psychology) , operator (biology) , pure mathematics , differential (mechanical device) , class (philosophy) , biochemistry , chemistry , repressor , artificial intelligence , computer science , economics , transcription factor , market economy , gene , engineering , aerospace engineering
This paper studies the question of the resolvent existence, as well as, the smoothness of elements from the definition domain (separability) of a class of hyperbolic differential operators defined in an unbounded domain with greatly increasing coefficients after a closure in the space L2(R2). Such a problem was previously put forward by I.M. Gelfand for elliptic operators. Here, we note that a detailed analysis shows that when studying the spectral properties of differential operators specified in an unbounded domain, the behavior of the coefficients at infinity plays an important role.