Uniqueness theorem and subharmonic test function

Subharmonic test functions and the distribution of zero sets of holomorphic functions

“…Throughout this article, D is a non-empty domain in R d , and a point o ∈ D or, in more general cases, a non-empty subset S o D, S o ∈ B(D), will play a role of an origin for D. The theory of distributions or generalized functions uses test finite positive functions to define the usual order relation on distributions or measures/charges. We consider various classes of test functions generated by subharmonic functions near the boundary ∂ D of D or on D\S o to study the order relation ≺ H on subharmonic functions [45], [46], [47], [43, 2.1], [40], [58], [41,…”

On a Blaschke-type condition for subharmonic functions with two sets of singularities on the boundary

“…1 The case of more general conditions on a function v and its associated measure was considered in the papers [10], [11], but these conditions do not look as clear as ours.…”

Affine Balayage of Measures and Distribution of Riesz Measures of Subharmonic Functions

“…Remark 8.1. Numerous methods and examples of constructing various classes of test subharmonic positive functions are described in articles [42], [49]. Test subharmonic alternatingsign functions can be obtained from them in the development of Example 5.5 and in the consideration of potentials for measure from such examples.…”