Identities for sums of characteristic values of entire matrix pencils

The paper deals with an entire matrix-valued function of a complex argument (an entire matrix pencil) f   of order ρ(f)<∞ρ(f)<∞. Identities for the following sums of the characteristic values zk(f)(k=1,2,…) of f are established:∑k=1∞1zkm(f)(m>ρ(f))and∑k=1∞Im1zk(f)2(ρ(f)<2).The suggested results are new even for polynomial pencils.