Displaying similar documents to “Commutative neutrix convolution products of functions”

On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator W k : = Δ + k x n x n on n is proved. In this note there is shown that in the cases k 0 , k 2 no other transforms of this kind exist and for case k = 2 , all such transforms are described.

On infinite composition of affine mappings

László Máté (1999)

Fundamenta Mathematicae

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 Let F i = 1 , . . . , N be affine mappings of n . It is well known that if there exists j ≤ 1 such that for every σ 1 , . . . , σ j 1 , . . . , N the composition (1) F σ 1 . . . F σ j is a contraction, then for any infinite sequence σ 1 , σ 2 , . . . 1 , . . . , N and any z n , the sequence (2) F σ 1 . . . F σ n ( z ) is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any z n and any σ = σ 1 , σ 2 , . . . belonging to some subshift Σ of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every σ = σ 1 , σ 2 , . . . Σ the composition (1) is a contraction....

Distances on the tropical line determined by two points

María Jesús de la Puente (2014)

Kybernetika

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Let p ' and q ' be points in n . Write p ' q ' if p ' - q ' is a multiple of ( 1 , ... , 1 ) . Two different points p and q in n / uniquely determine a tropical line L ( p , q ) passing through them and stable under small perturbations. This line is a balanced unrooted semi-labeled tree on n leaves. It is also a metric graph. If some representatives p ' and q ' of p and q are the first and second columns of some real normal idempotent order n matrix A , we prove that the tree L ( p , q ) is described by a matrix F , easily obtained from A . We also...

On the preservation of separation axioms in products

Milan Z. Grulović, Miloš S. Kurilić (1992)

Commentationes Mathematicae Universitatis Carolinae

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We give sufficient and necessary conditions to be fulfilled by a filter Ψ and an ideal Λ in order that the Ψ -quotient space of the Λ -ideal product space preserves T k -properties ( k = 0 , 1 , 2 , 3 , 3 1 2 ) (“in the sense of the Łos theorem”). Tychonoff products, box products and ultraproducts appear as special cases of the general construction.

A problem of Galambos on Engel expansions

Jun Wu (2000)

Acta Arithmetica

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1. Introduction. Given x in (0,1], let x = [d₁(x),d₂(x),...] denote the Engel expansion of x, that is, (1) x = 1 / d ( x ) + 1 / ( d ( x ) d ( x ) ) + . . . + 1 / ( d ( x ) d ( x ) . . . d n ( x ) ) + . . . , where d j ( x ) , j 1 is a sequence of positive integers satisfying d₁(x) ≥ 2 and d j + 1 ( x ) d j ( x ) for j ≥ 1. (See [3].) In [3], János Galambos proved that for almost all x ∈ (0,1], (2) l i m n d n 1 / n ( x ) = e . He conjectured ([3], P132) that the Hausdorff dimension of the set where (2) fails is one. In this paper, we prove this conjecture: Theorem. d i m H x ( 0 , 1 ] : ( 2 ) f a i l s = 1 . We use L¹ to denote the one-dimensional Lebesgue measure on (0,1] and d i m H to denote...

Baireness of C k ( X ) for ordered X

Michael Granado, Gary Gruenhage (2006)

Commentationes Mathematicae Universitatis Carolinae

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We show that if X is a subspace of a linearly ordered space, then C k ( X ) is a Baire space if and only if C k ( X ) is Choquet iff X has the Moving Off Property.