On a problem by Shapiro.
On a problem concerning quasianalytic local rings
Let (ₙ)ₙ be a quasianalytic differentiable system. Let m ∈ ℕ. We consider the following problem: let and f̂ be its Taylor series at . Split the set of exponents into two disjoint subsets A and B, , and decompose the formal series f̂ into the sum of two formal series G and H, supported by A and B, respectively. Do there exist with Taylor series at zero G and H, respectively? The main result of this paper is the following: if we have a positive answer to the above problem for some m ≥ 2, then...
On a problem concerning uniform ;imits of Darboux functions
On a problem of Davison.
On a problem of J. Schnitzer
On a problem of Matkowski
We solve Matkowski's problem for strictly comparable quasi-arithmetic means.
On a problem of Mazur from "The Scottish Book" concerning second partial derivatives
We comment on a problem of Mazur from “The Scottish Book" concerning second partial derivatives. We prove that if a function f(x,y) of real variables defined on a rectangle has continuous derivative with respect to y and for almost all y the function has finite variation, then almost everywhere on the rectangle the partial derivative exists. We construct a separately twice differentiable function whose partial derivative is discontinuous with respect to the second variable on a set of positive...
On a problem of R. C. Baker
On a problem of V. Pták
On a proof of the Erdős-Monk theorem.
On a property of convex functions.
On a property of Gram's determinant.
On a question of Milman and Alesker concerning the monotonicity of a domain functional.
On a residual set of continuous functions
On a reverse of a Hardy-Hilbert type inequality.
On a reverse of Jessen's inequality for isotonic linear functionals.
On a semigroup of modular functions with involution.
On a set in under coordinate transformations
On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball
2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05We study a singular value problem and the boundary Harnack principle for the fractional Laplacian on the exterior of the unit ball.
On a strengthened Hardy-Hilbert inequality.