The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
The properties of the root functions are studied for an arbitrary operator generated in L2(−1, 1) by the operation with involution of the form Lu = −u″(x)+αu″(−x)+q(x)u(x)+ qν(x)u(ν(x)), where α ∈ (−1, 1), ν(x) is an absolutely continuous involution of the segment [−1, 1] and the coefficients q(x) and qν(x) are summable functions on (−1, 1). Necessary and sufficient conditions are obtained for the...
For the equation αu″(-x) - u″(x) = λu(x), ™1 < x < 1, where α ∈ (™1, 1), we study the problem with the nonlocal conditions u(™1) = 0, u′(™1) = u′(1). We show that if $$r = \sqrt {\left( {1 - \alpha } \right)/\left( {1 + \alpha } \right)} $$ is irrational, then the system of eigenfunctions is complete and minimal in L2(™1, 1) but is not a basis. For rational r, we indicate a method for...