All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 8 Next

Displaying 141 – 160 of 2726

Showing per page

A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix

Fuad Kittaneh (2003)

Studia Mathematica

It is shown that if A is a bounded linear operator on a complex Hilbert space, then w ( A ) ≤ 1 / 2 ( | | A | | + | | A ² | | 1 / 2 ) , where w(A) and ||A|| are the numerical radius and the usual operator norm of A, respectively. An application of this inequality is given to obtain a new estimate for the numerical radius of the Frobenius companion matrix. Bounds for the zeros of polynomials are also given.

A polynomial with 2k critical values at infinity

Janusz Gwoździewicz, Maciej Sękalski (2004)

Annales Polonici Mathematici

We construct a polynomial f:ℂ² → ℂ of degree 4k+2 with no critical points in ℂ² and with 2k critical values at infinity.

A proof of the Livingston conjecture for the fourth and the fifth coefficient of concave univalent functions

Karl-Joachim Wirths (2004)

Annales Polonici Mathematici

Let D denote the open unit disc and f:D → ℂ̅ be meromorphic and injective in D. We further assume that f has a simple pole at the point p ∈ (0,1) and an expansion f ( z ) = z + ∑ n = 2 ∞ a ₙ ( f ) z ⁿ , |z| < p. In particular, we consider f that map D onto a domain whose complement with respect to ℂ̅ is convex. Because of the shape of f(D) these functions will be called concave univalent functions with pole p and the family of these functions is denoted by Co(p). It is proved that for p ∈ (0,1) the domain of variability of the coefficient...

A pure smoothness condition for Radó’s theorem for α -analytic functions

Abtin Daghighi, Frank Wikström (2016)

Czechoslovak Mathematical Journal

Let Ω ⊂ ℂ n be a bounded, simply connected ℂ -convex domain. Let α ∈ ℤ + n and let f be a function on Ω which is separately C 2 α j - 1 -smooth with respect to z j (by which we mean jointly C 2 α j - 1 -smooth with respect to Re z j , Im z j ). If f is α -analytic on Ω ∖ f - 1 ( 0 ) , then f is α -analytic on Ω . The result is well-known for the case α i = 1 , 1 ≤ i ≤ n , even when f a priori is only known to be continuous.

Currently displaying 141 – 160 of 2726