Analytic theory of polynomials

By Q. I. Rahman, G. Schmeisser. 2002

1,037 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/257f601154c4bcda48268a09caccaa1973fe0388

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Citations in the corpus

Invariant distances and metrics in complex analysis-revisited (2005, background): “[Rah-Sch 2002]) f−1(0) ⊂ E iff |p| < 1 and the root of the polynomial”
The Lee-Yang and Pólya-Schur programs. I. Linear operators preserving stability (2008, background): “In particular, in [41] Pólya and Schur characterized all diagonal operators with this property (so-called multiplier sequences), which paved the way for numerous subsequent investigations [7, 9, 15, 16, 17, 19, 26, 32, 35, 40, 43, 50].”
Polya-Schur master theorems for circular domains and their boundaries (2006, methodology): “The following theorem is a version of the classical Hermite-Biehler theorem [38].”
Applications of stable polynomials to mixed determinants: Johnson's conjectures, unimodality, and symmetrized Fischer products (2006, unknown): “[21].”
Multivariate stable polynomials: theory and applications (2009, unknown): “1b of [14]).”
Polynomials with the half-plane property and matroid theory (2006, background): “ the zeros of the polynomial 0 interlaces the zeros of any (non-zero) real-rooted polynomial f, and write 0 ≪ f and f ≪ 0. The Hermite-Biehler Theorem characterizes univariate stable polynomials, see [28]. Theorem 5.1 (Hermite-Biehler). Let f = h + ig ∈ C[z] where h,g ∈ R[z]. Then f is stable if and”
Optimality and uniqueness of the Leech lattice among lattices (2004, background): “and is congruent to it modulo 2. For (a, ∞) one can simply use p(a + z). This result is sometimes known as Jacobi’s rule of signs (see Corollary 10.1.13 in [ RS , p. 320]).”
Negative dependence and the geometry of polynomials (2007, background): “The famous Grace-Walsh-Szegö coincidence theorem [32, 66, 74] is stated next.”
Iterated sequences and the geometry of zeros (2009, background): “1 The Grace–Walsh–Szegő Theorem is undoubtably one of the most useful theorems governing the location of zeros of polynomials, see [13].”