Evaluation of two trigonometric sums
Everywhere divergent Fourier series
Exact Kronecker constants of Hadamard sets
A set S of integers is called ε-Kronecker if every function on S of modulus one can be approximated uniformly to within ε by a character. The least such ε is called the ε-Kronecker constant, κ(S). The angular Kronecker constant is the unique real number α(S) ∈ [0,1/2] such that κ(S) = |exp(2πiα(S)) - 1|. We show that for integers m > 1 and d ≥ 1, and α1,m,m²,... = 1/(2m).
Exakte Größenordnung für das Randverhalten des Poissonschen Integrals von BMO-Funktionen und VMO-Funktionen
Examples of Λ(4) sets E and a graph structure in E x E
Existence of almost automorphic solutions to some classes of nonautonomous higher-order differential equations.
Existence of doubly-weighted pseudo almost periodic solutions to non-autonomous differential equations.
Existence of large ε-Kronecker and FZI₀(U) sets in discrete abelian groups
Let G be a compact abelian group with dual group Γ and let ε > 0. A set E ⊂ Γ is a “weak ε-Kronecker set” if for every φ:E → there exists x in the dual of Γ such that |φ(γ)- γ(x)| ≤ ε for all γ ∈ E. When ε < √2, every bounded function on E is known to be the restriction of a Fourier-Stieltjes transform of a discrete measure. (Such sets are called I₀.) We show that for every infinite set E there exists a weak 1-Kronecker subset F, of the same cardinality as E, provided there are not “too many”...
Existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations.
Experimental approaches to Kuttner's problem.
Exponential approximation on the real line
Exponential sums with coefficients or and concentrated norms
A sum of exponentials of the form , where the are distinct integers is called an idempotent trigonometric polynomial (because the convolution of with itself is ) or, simply, an idempotent. We show that for every and every set of the torus with there are idempotents concentrated on in the sense. More precisely, for each there is an explicitly calculated constant so that for each with and one can find an idempotent such that the ratio is greater than . This is in fact...
Extension de fonctions de type positif et entropie associée. Cas multidimensionnel
Extension of a Theorem of Fejér to Double Fourier-Stieltjes Series.
Extension of analytic number theory and the theory of regularized harmonic series from Dirichlet series to Bessel series.
Extension sets for real analytic functions and applications to Radon transforms.
Extensions of a Fourier multiplier theorem of Paley, II
Extensions of the Heisenberg-Weyl inequality.
Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces.
Extreme positive definite double sequences which are not moment sequences.
From the fact that the two-dimensional moment problem is not always solvable, we can deduce that there must be extreme ray generators of the cone of positive definite double sequences which are nor moment sequences. Such an argument does not lead to specific examples. In this paper it is shown how specific examples can be constructed if one is given an example of an N-extremal indeterminate measure in the one-dimensional moment problem (such examples exist in the literature). Konrad Schmüdgen had...