Displaying similar documents to “Some results on the product of distributions and the change of variable”

Best approximations and porous sets

Simeon Reich, Alexander J. Zaslavski (2003)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let D be a nonempty compact subset of a Banach space X and denote by S ( X ) the family of all nonempty bounded closed convex subsets of X . We endow S ( X ) with the Hausdorff metric and show that there exists a set S ( X ) such that its complement S ( X ) is σ -porous and such that for each A and each x ˜ D , the set of solutions of the best approximation problem x ˜ - z min , z A , is nonempty and compact, and each minimizing sequence has a convergent subsequence.

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

Similarity:

1. Introduction. Let p be a prime number and p the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, k a p -extension of k, k n the nth layer of k / k , and A n the p-Sylow subgroup of the ideal class group of k n . Iwasawa proved the following well-known theorem about the order A n of A n : Theorem A (Iwasawa). Let k / k be a p -extension and A n the p-Sylow subgroup of the ideal class group of k n , where k n is the n th layer of k / k . Then there exist integers λ = λ ( k / k ) 0 , μ = μ ( k / k ) 0 , ν = ν ( k / k ) , and n₀ ≥ 0...

On the eigenvalues of a Robin problem with a large parameter

Alexey Filinovskiy (2014)

Mathematica Bohemica

Similarity:

We consider the Robin eigenvalue problem Δ u + λ u = 0 in Ω , u / ν + α u = 0 on Ω where Ω n , n 2 is a bounded domain and α is a real parameter. We investigate the behavior of the eigenvalues λ k ( α ) of this problem as functions of the parameter α . We analyze the monotonicity and convexity properties of the eigenvalues and give a variational proof of the formula for the derivative λ 1 ' ( α ) . Assuming that the boundary Ω is of class C 2 we obtain estimates to the difference λ k D - λ k ( α ) between the k -th eigenvalue of the Laplace operator with...