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Full-Text Articles in Physical Sciences and Mathematics
Properties In $L_P$ Of Root Functions For A Nonlocal Problem With Involution, Leonid Kritskov, Makhmud Sadybekov, Abdizhahan Sarsenbi
Properties In $L_P$ Of Root Functions For A Nonlocal Problem With Involution, Leonid Kritskov, Makhmud Sadybekov, Abdizhahan Sarsenbi
Turkish Journal of Mathematics
The spectral problem $-u''(x)+\alpha u''(-x)=\lambda u(x)$, $-1$%lt; $x$ < $1$, with nonlocal boundary conditions $u(-1)=\beta u(1)$, $u'(-1)=u'(1)$, is studied in the spaces $L_p(-1,1)$ for any $\alpha\in (-1,1)$ and $\beta\ne\pm 1$. It is proved that if $r=\sqrt{(1-\alpha)/(1+\alpha)}$ is irrational then the system of its eigenfunctions is complete and minimal in $L_p(-1,1)$ for any $p>1$, but does not form a basis. In the case of a rational value of $r$, the way of supplying this system with associated functions is specified to make all the root functions a basis in $L_p(-1,1)$.
Basicity Of A System Of Exponents With A Piecewise Linear Phase In Morrey-Type Spaces, Bilal Bilalov, Fidan Seyidova
Basicity Of A System Of Exponents With A Piecewise Linear Phase In Morrey-Type Spaces, Bilal Bilalov, Fidan Seyidova
Turkish Journal of Mathematics
In this paper a perturbed system of exponents with a piecewise linear phase depending on two real parameters is considered. The sufficient conditions for these parameters are found, under which the considered system of exponents is complete, minimal, or it forms a basis for a Morrey-type space.