Instead of applying (1) and the linear map equation (3), the nonlinear Bloch-LSQR solution was modeled by populating the matrix E whilst calling the Bloch function
written in Matlab script, followed by the solution of (2) by using the lsqr method in Matlab.
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.
Ma, Bloch functions on strongly pseudoconvex domains, Indiana Univ.
Timoney, Bloch functions of several variables I, Bull.
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.