The Cauchy problem for evolution equations with the Bessel operator of infinite order. I (Q1956624)

Singular evolution equations of infinite order represent natural generalization of singular parabolic equations and contain the Bessel operator of infinite order with \(\varphi (B_\nu)=\sum_{k=0}^\infty c_k B^k_\nu\) instead of the relevant finite sum. Here \(B_\nu\) is the Bessel operator of order \(\nu> -1/2\). The paper contains necessary and sufficient conditions under which the Bessel operator of infinite order is bounded in certain spaces. The relevant convolution operators are studied.