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For the self-adjoint operator of the $p$th derivative, a system offundamental solutions is constructed. This system is analogues to the classicalsystem of sines and cosines. The properties of such functions are studied.Classes of self-adjoint boundary conditions are described. For the operator ofthe third derivative, the resolvent is calculated and an orthonormal basis ofeigenfunctions is given.

$p$-Hyperbolic Zolotarev Functions in Boundary Value Problems for a $p\,$th order Differential Operator