Displaying similar documents to “Positive solutions of a renewal equation”

Carathéodory balls and norm balls in H p , n = z n : z p < 1

Binyamin Schwarz, Uri Srebro (1996)

Banach Center Publications

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It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on H p , n = z n : z p < 1 which are balls with respect to the complex l p norm in n are those centered at the origin.

The exceptional set of Goldbach numbers (II)

Hongze Li (2000)

Acta Arithmetica

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1. Introduction. A positive number which is a sum of two odd primes is called a Goldbach number. Let E(x) denote the number of even numbers not exceeding x which cannot be written as a sum of two odd primes. Then the Goldbach conjecture is equivalent to proving that E(x) = 2 for every x ≥ 4. E(x) is usually called the exceptional set of Goldbach numbers. In [8] H. L. Montgomery and R. C. Vaughan proved that E ( x ) = O ( x 1 - Δ ) for some positive constant Δ > 0 . I n [ 3 ] C h e n a n d P a n p r o v e d t h a t o n e c a n t a k e Δ > 0 . 01 . I n [ 6 ] , w e p r o v e d t h a t E ( x ) = O ( x 0 . 921 ) . In this paper we prove the following...

The homotopy groups of the L2 -localization of a certain type one finite complex at the prime 3

Yoshitaka Nakazawa, Katsumi Shimomura (1997)

Fundamenta Mathematicae

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For the Brown-Peterson spectrum BP at the prime 3, v 2 denotes Hazewinkel’s second polynomial generator of B P * . Let L 2 denote the Bousfield localization functor with respect to v 2 - 1 B P . A typical example of type one finite spectra is the mod 3 Moore spectrum M. In this paper, we determine the homotopy groups π * ( L 2 M X ) for the 8 skeleton X of BP.

Qualitative investigation of nonlinear differential equations describing infiltration of water

Xingbao Wu (1995)

Annales Polonici Mathematici

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A nonlinear differential equation of the form (q(x)k(x)u')' = F(x,u,u') arising in models of infiltration of water is considered, together with the corresponding differential equation with a positive parameter λ, (q(x)k(x)u')' = λF(x,u,u'). The theorems about existence, uniqueness, boundedness of solution and its dependence on the parameter are established.

Property C'', strong measure zero sets and subsets of the plane

Janusz Pawlikowski (1997)

Fundamenta Mathematicae

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Let X be a set of reals. We show that  • X has property C" of Rothberger iff for all closed F ⊆ ℝ × ℝ with vertical sections F x (x ∈ X) null, x X F x is null;  • X has strong measure zero iff for all closed F ⊆ ℝ × ℝ with all vertical sections F x (x ∈ ℝ) null, x X F x is null.

An extension of a theorem of Marcinkiewicz and Zygmund on differentiability

S. Mukhopadhyay, S. Mitra (1996)

Fundamenta Mathematicae

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Let f be a measurable function such that Δ k ( x , h ; f ) = O ( | h | λ ) at each point x of a set E, where k is a positive integer, λ > 0 and Δ k ( x , h ; f ) is the symmetric difference of f at x of order k. Marcinkiewicz and Zygmund [5] proved that if λ = k and if E is measurable then the Peano derivative f ( k ) exists a.e. on E. Here we prove that if λ > k-1 then the Peano derivative f ( [ λ ] ) exists a.e. on E and that the result is false if λ = k-1; it is further proved that if λ is any positive integer and if the approximate Peano...

Note on the congruence of Ankeny-Artin-Chowla type modulo p²

Stanislav Jakubec (1998)

Acta Arithmetica

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The results of [2] on the congruence of Ankeny-Artin-Chowla type modulo p² for real subfields of ( ζ p ) of a prime degree l is simplified. This is done on the basis of a congruence for the Gauss period (Theorem 1). The results are applied for the quadratic field ℚ(√p), p ≡ 5 (mod 8) (Corollary 1).

Spaces of upper semicontinuous multi-valued functions on complete metric spaces

Katsuro Sakai, Shigenori Uehara (1999)

Fundamenta Mathematicae

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Let X = (X,d) be a metric space and let the product space X × ℝ be endowed with the metric ϱ ((x,t),(x’,t’)) = maxd(x,x’), |t - t’|. We denote by U S C C B ( X ) the space of bounded upper semicontinuous multi-valued functions φ : X → ℝ such that each φ(x) is a closed interval. We identify φ U S C C B ( X ) with its graph which is a closed subset of X × ℝ. The space U S C C B ( X ) admits the Hausdorff metric induced by ϱ. It is proved that if X = (X,d) is uniformly locally connected, non-compact and complete, then U S C C B ( X ) is homeomorphic...