Distance between a maximum modulus point and zero set of an analytic function
نویسندگان
چکیده
منابع مشابه
On the Mean Modulus of an Analytic Function
For fixed ƒ and r this mean modulus Mt(r;f) as a function of / is continuous, nonnegative, nondecreasing, and is bounded above by the maximum modulus of ƒ on C(r) [l, 2 ] . 1 Therefore the limit of Mt(r;f) exists as /—>0 and /—» oo. This limit is defined to be the mean modulus of ƒ on C(r) of order 0 and of order oo respectively. I t may be shown that the mean modulus of order 0 is the geometri...
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Large deviations for the zero set of an analytic function with diffusing coefficients
The hole probability that the zero set of the time dependent planar Gaussian analytic function fC(z, t) = ∞ ∑ n=0 an(t) zn √ n! , (1) where an(t) are i.i.d. complex valued Ornstein-Uhlenbeck processes, does not intersect a disk of radius R for all t ∈ [0, T ] decays like exp(−TecR2). This result sharply differentiates the zero set of fC from a number of canonical evolving planar point processes...
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Let f be analytic on the compact set E ⊂ C , of positive transfinite diameter and let Cr denote the largest equipotential curve of E such that f is analytic within Cr. Generally, the growth of an entire function is measured in terms of its order and type. Here we have established the relations between maximum modulus, maximum term and interpolation error of best uniform approximation to a funct...
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ژورنال
عنوان ژورنال: Matematychni Studii
سال: 2019
ISSN: 1027-4634
DOI: 10.30970/ms.52.1.10-23