Интегральные тождества на сфере для нормальных производных полигармонических функций

Identities for the integrals over the unit sphere of the products of linear combinations of normal derivatives of polyharmonic function in the unit ball and homogeneous harmonic polynomials are obtained. Basing on these identities the necessary conditions for the values on the unit sphere of polynomials on normal derivatives of polyharmonic functions are derived. Illustrative examples are given.