Abstract:
We find the necessary and sufficient conditions for the completeness and minimality in the space L2(0;1) of system (√xρkJν(xρk):k∈N) generated by Bessel function of the first kind of index ν⩾−1/2. Moreover, we establish a criterion for the completeness and minimality of system (x−2√xρkJ3/2(xρk):k∈N) in the space L2((0;1);x2dx).