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In this paper we propose to discuss some relationships between the classical Traveling Salesman Problem (TSP), Litlewood-Paley theory, and harmonic measure. This circle of ideas is also closely related to the theory of Cauchy integrals on Lipschitz graphs, and this aspect is discussed more fully in the paper of David and Semmes [2] in this proceedings. The main differences between the subjects in [2] and this paper are that the results here are valid for one dimensional sets, whereas [2] treats...
The purpose of this paper is to establish a theorem which answers a conjecture of Paley on the distribution of values of Hadamard lacunary series and which is useful to study the Peano curve property of such series.
We consider the zero distribution of difference-differential polynomials of meromorphic functions and present some results which can be seen as the discrete analogues of the Hayman conjecture. In addition, we also investigate the uniqueness of difference-differential polynomials of entire functions sharing one common value. Our theorems improve some results of Luo and Lin [J. Math. Anal. Appl. 377 (2011), 441-449] and Liu, Liu and Cao [Appl. Math. J. Chinese Univ. 27 (2012), 94-104].
Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20The classical Cauchy-Hadamard, Abel and Tauber theorems provide
useful information on the convergence of the power series in complex plane.
In this paper we prove analogous theorems for series in the generalized
Lommel-Wright functions with 4 indices. Results for interesting special
cases of series involving Bessel, Bessel-Maitland, Lommel and Struve functions,
are derived.We provide also a new asymptotic formula for the generalized
...
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