Titus Hilberdink

Matrices with multiplicative entries

We study matrices (both finite and infinite) whose entries are a multiplicative function of two variables. We show that the operators represented by such matrices are infinite tensor products over the primes, like an Euler product. Applications to finding the eigenvalues explicitly of arithmetical matrices are given; also Multiplicative Toeplitz and Hankel operators whose entries are of the form f(i/j) and g(ij) respectively are discussed.