LAUSR

For a certain class of sequences with multiple terms $$\{\underbrace{\lambda _1,\lambda _1,\ldots ,\lambda _1}_{\mu _1 - times}, \underbrace{\lambda _2,\lambda _2,\ldots ,\lambda _2}_{\mu _2 - times},\ldots \}$${λ1,λ1,…,λ1⏟μ1-times,λ2,λ2,…,λ2⏟μ2-times,…} in the right half-plane $$\mathbb {C}_+$$C+, and a doubly-indexed sequence $$\{d_{n,k}{:}\, n\in \mathbb {N},\, k=0,1,\ldots ,\mu _n-1\}$${dn,k:n∈N,k=0,1,…,μn-1} of complex numbers satisfying certain growth conditions, we consider an interpolation problem $$\begin{aligned} f^{(k)}(\lambda _n)=d_{n,k}\qquad n\in \mathbb {N},\quad k=0,1,\ldots ,\mu _n-1, \end{aligned}$$f(k)(λn)=dn,kn∈N,k=0,1,…,μn-1,where f is a bounded analytic function in $$\mathbb {C}_+$$C+, belonging to the Hardy spaces $$H^1 (\mathbb {C}_+)$$H1(C+) and $$H^2 (\mathbb {C}_+)$$H2(C+).