  The properties of the transfer-matrix of U(1) lattice gauge theory in the
Fourier basis are explored. Among other statements it is shown: 1) the
transfer-matrix is block-diagonal, 2) all consisting vectors of a block are
known based on an arbitrary block vector, 3) the ground-state belongs to the
zero-mode's block. The emergence of maximum-points in matrix-elements as
functions of the gauge coupling is clarified. Based on explicit expressions for
the matrix-elements we present numerical results as tests of our statements.
