• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.507-530
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• 2018

It is shown that for a non-unitary twist of a Fuchsian group, which is unitary at the cusps, Eisenstein series converge in some half-plane. It is shown that invariant integral operators provide a spectral decomposition of the space of cusp forms and that Eisenstein series admit a meromorphic continuation.

• Nuclear Engineering and Technology
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• v.1 no.2
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• pp.103-106
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• 1969

A new representation for the Dirac equation, which may be appropriate to describe the interaction of the charged particle with the electric field, is derived by introducing a gauge-independent unitary transformation. It is shown that in this representation the effective Hamiltonian without potentials has a new feature in the non-relativistic limit.