Subsequences of zeros for classes of entire functions of exponential type distinguished by growth restrictions

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

“…{x} is called a Jensen potential on O with pole at x ∈ O if this function V satisfies conditions (6.17) [18,3], [1], [37], [58], [39, Definition 8], [52, IIIC], [41], [47], [6]. The class of all Jensen potential on O with pole at x ∈ O denote by P J x (O) ⊂ AS x (O).…”

“…In connection with the quadrature domains, see very informative overview [22,3] and bibliography in it. Example 5.1 ([18, 3], [51], [52], [14], [15], [11], [23], [27]- [43], [47], [6]). If a measure µ ∈ Meas + cmp (O) is a balayage of the Dirac measure δ x for sbh(O), where x ∈ O, then this measure µ is called a Jensen measure for x.…”

Poisson-Jensen Formulas and Balayage of Measures

“…(2.11) If x ∈ O and δ x sbh(O) ω, then this measure ω is called a Jensen measure on O at x [15, 3], [43], [44], [12], [13], [51], [10], [20], [21], [24], [42], [7], [38]. The class of these measures is denoted by J x (O), and properties (2.11) are supplemented by the positivity property pt ω−δx ≥ 0 on R d ∞ \x for all measures ω ∈ J x (O) ⊂ AS x (O).…”

“…A positive Arens -Singer potential is called a Jensen potential on O with pole at x ∈ O [15, 3], [1], [35], [47], [36, Definition 8], [44, IIIC], [37], [42], [7]. We denote by JP x (O) the class of all Jensen potentials on O with pole at x ∈ O.…”

Classical Balayage of Charges and Measures

“…These rules are described in detail in L. Schwartz's monograph [22, Vol. I,Ch.IV, § 6] and we do not dwell on them here, although here interesting questions arise, for example, for the Bernstein -Paley -Wiener -Mary Cartwright classes of entire functions [11], [16], [1], [15] etc.…”