Asymptotic tracts of harmonic functions II

Asymptotic Behavior of Infinity Harmonic Functions Near an Isolated Singularity

In this paper, we prove that if n ≥ 2 and x0 is an isolated singularity of a non-negative infinity harmonic function u, then either x0 is a removable singularity of u or u(x) = u(x0) + c|x − x0| + o(|x − x0|) near x0 for some fixed constant c = 0. In particular, if x0 is nonremovable, then u has a local maximum or a local minimum at x0. We also prove a Bernstein-type theorem, which asserts that...

On the axiomatic of harmonic functions II

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A lower estimate of harmonic functions

We shall give a lower estimate of harmonic‎ ‎functions of order greater than one in a half space‎, ‎which‎ ‎generalize the result obtained by B‎. ‎Ya‎. ‎Levin in a half plane‎.

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Asymptotic error expansion of wavelet approximations of smooth functions II

We generalize earlier results concerning an asymptotic error expansion of wavelet approximations. The properties of the monowavelets, which are the building blocks for the error expansion, are studied in more detail, and connections between spline wavelets and Euler and Bernoulli polynomials are pointed out. The expansion is used to compare the error for different wavelet families. We prove tha...