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A note on some expansions of p-adic functions

Grzegorz Szkibiel (1992)

Acta Arithmetica

Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by ( ϕ ₘ ) m ∈ ℕ ₀ . The system ( ϕ ₘ ) m ∈ ℕ ₀ is defined in the space C(ℤₚ,ℂₚ) of ℂₚ-valued continuous functions on ℤₚ. J. Rutkowski has also considered some questions concerning expansions of functions from C(ℤₚ,ℂₚ) with respect to ( ϕ ₘ ) m ∈ ℕ ₀ . This paper is a remark to Rutkowski’s paper. We define another system ( h ₙ ) n ∈ ℕ ₀ in C(ℤₚ,ℂₚ), investigate its properties and compare it to the system defined by Rutkowski. The system...

A note on strong pseudoconvexity

Vsevolod Ivanov (2008)

Open Mathematics

A strongly pseudoconvex function is generalized to non-smooth settings. A complete characterization of the strongly pseudoconvex radially lower semicontinuous functions is obtained.

A Note on the Men'shov-Rademacher Inequality

Witold Bednorz (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

We improve the constants in the Men’shov-Rademacher inequality by showing that for n ≥ 64, E ( s u p 1 ≤ k ≤ n | ∑ i = 1 k X i | ² ≤ 0 . 11 ( 6 . 20 + l o g ₂ n ) ² for all orthogonal random variables X₁,..., Xₙ such that ∑ k = 1 n E | X k | ² = 1 .

A note on the Poincaré inequality

Alireza Ranjbar-Motlagh (2003)

Studia Mathematica

The Poincaré inequality is extended to uniformly doubling metric-measure spaces which satisfy a version of the triangle comparison property. The proof is based on a generalization of the change of variables formula.

A note on the scalar Haffian.

Heinz Neudecker (2000)

Qüestiió

In this note a uniform transparent presentation of the scalar Haffian will be given. Some well-known results will be generalized. A link will be established between the scalar Haffian and the derivative matrix as developed by Magnus and Neudecker.

A note on the three-segment problem

Martin Doležal (2009)

Mathematica Bohemica

We improve a theorem of C. L. Belna (1972) which concerns boundary behaviour of complex-valued functions in the open upper half-plane and gives a partial answer to the (still open) three-segment problem.

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.

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