The Bloch functions can only allow the four wave vector to assume the following quantized values:
For large values of n the Bloch functions statisfy the condition
Note that Theorem 1 not only characterizes the composition operators mapping logarithmic Bloch functions into the Hardy space but also introduces a kind of g-function.
Rudin, "Bloch functions, BMO, and boundary zeros," Indiana University Mathematics Journal, vol.
In the LCAO technique, each crystalline orbital is built from the linear combination of
Bloch functions. The
Bloch functions are defined in terms of local functions constructed from the atom-centered certain number of Gaussian functions.
Aulaskari and P Lappan, Additive automorphic functions and Bloch functions, Canadian J.
Makhmutov, Integral characterizations of Bloch functions, New Zealand Journal of Mathematics, Vol 26 (1997), 201-212.
Yanagihara, "Sharp distortion estimate for locally schlicht
Bloch functions," The Bulletin of the London Mathematical Society, vol.
Miralles, "
Bloch functions on the unit ball of an infinite dimensional Hilbert space," Journal of Functional Analysis, vol.