Stochastic optimization on complex variables and pure-state quantum tomography
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DOI: 10.1038/s41598-019-52289-0
Abstract: Real-valued functions of complex arguments violate the Cauchy-Riemann conditions and, consequently, do not have Taylor series expansion. Therefore, optimization methods based on derivatives cannot be directly applied to this class of functions. This is circumvented… read more here.
Keywords: stochastic optimization; quantum tomography; optimization; complex arguments ... See more keywords
Inequalities for gamma and q-gamma functions of complex arguments
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DOI: 10.1142/s0219530516500093
Abstract: We prove that the function Γ(x + a)Γ(x + b)/|Γ(x + c + iy)|2,a + b = 2c, and its q-analogue are of the form e−h(x,y) and h is completely monotonic in x. In particular… read more here.
Keywords: gamma functions; functions complex; complex arguments; inequalities gamma ... See more keywords