Indagationes Mathematicae (Proceedings)最新文献

In [3]-[7] Woodcock developed a Fourier theory for continuously differentiable functions defined on the set of p-adic integers. In this paper his theory is continued by giving a characterization of the image of the Fourier transformation. Also a special form of continuity of the inverse Fourier transformation is proved and, as an application, the Fourier transform of an antiderivative of a function is calculated.

We generalize the main result of [21] to Riesz spaces. Let X and Y be Riesz spaces with σ-complete Boolean algebras of projection bands. If X and Y are each Riesz isomorphic to a projection band of the other space then the spaces are Riesz isomorphic. As an application of the above theorem we give an example of non-Riesz isomorphic Banach lattices such that: (1) their order (= topological) duals are Riesz isomorphic and (2) each of them is Riesz isomorphic to a projection band of the other one.

Let (A, %plane1D;49C;, μ) be a finite measure space, and let Ω_{µ, w}⁺f denote the set of all nonnegative real-valued %plane1D;49C;-measurable functions on A weaklymajorized by a nonnegative function f, in the sense of Hardly, Littlewood and Pólya. For a nonatomic µ, the extreme points ofΩ_{µ, w} ⁺f are shown to be the nonnegativefunctions obtained by taking a fraction (1−θ) of the largest values of and arranging them in any way on any subset of A of measure(1−θ), with values elsewhere set equal to zero. Topological properties of these extreme points are given.

Let A_n/B_n, n = 1,2,… denote the sequence of convergents of the nearest integer continued fraction expansion of the irrational number x, and defineΘ_n(x): B_n|B_nx − A_n|, n = 1,2,…. In this paper the distribution of the two-dimensional sequence (Θ_n(x), Θ_n+1(x)), n = 1,2,… is determined for almost all x.

Various corollaries are obtained, for instance Sendov's analogue of Vahlen's theorem for the nearest integer continued fraction. The present method is an extension of the work by H. Jager on the corresponding problem for the regular continued fraction expansion.

We consider certain generalisation of the resultant of two polynomials in one variable. Using the Schur symmetricfunctions we describe the ideal of all polynomials in the coefficients of two equations, which vanish if these equations haver+1 roots in common, where r≥0. We discuss also related (classical)criterions giving the conditions when two equations have r+1 roots in common, where r≥0.

Let P denote the differentiation operator i d/dx and %plane1D;4AC; the operator of multiplication by x in L₂(ℝ). With suitable domains the operators P and %plane1D;4AC; are self-adjoint. In this paper, characterizations of the space S_α^β of Gelfand and Shilov are derived in terms of the operators P and %plane1D;4AC;. The main result is that S_α=D^ω(|Q|^1/α)∩ D^∞(P), S^β = D^∞(%plane1D;4AC;)D^ω(|P|^1/β) and S_α^β = D^ω(|%plane1D;4AC;|^1/β) ∩ ∩ D^ω (|P|^1/β. Here D^∞(·) denote the C^∞ - and the analyticity domain of the operator between brackets.

In ZBuRe], Burkill et al. introduce the test function space T. Our results imply that T = _1/2^1/2. That is, the corresponding space of generalized functions can be identified with the space of generalized functions introduced by De Bruijn in ZBr1].

It is shown that the “trace-free” differential invariants of triples of vector 1-forms form a space of dimension 13. Twelve of these are accounted for by constructions based on the known bilinear “bracket” of vector 1-forms. We find one that is new, and exhibit it in various forms, including one that shows an unusual symmetry: it alternates in the three vector 1-forms and is a tensor of type (1,2), symmetric in its covariant part. Two-dimensional manifolds admit yet another new invariant.