منابع مشابه
A Sharp Form of the Virial Theorem
In its classical form the Virial Theorem concerns the behavior of a system S of n mass particles acting under Newtonian attraction in such a fashion that the center of mass 0 remains fixed and the potential energy V satisfies V> — <*> for all positive time t. The latter condition, which is not always stated explicitly, guarantees the analyticity of the coordinates of the particles in the indepe...
متن کاملA Sharp Form of Whitney’s Extension Theorem
0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 1. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2. Statement of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3. Order Relations Involving Multi–indices . . . . . . . ....
متن کاملA Sharp Form of the Cramér–wold Theorem
The Cramér–Wold theorem states that a Borel probability measure P on R is uniquely determined by its one-dimensional projections. We prove a sharp form of this result, addressing the problem of how large a subset of these projections is really needed to determine P . We also consider extensions of our results to measures on a separable Hilbert space. As an application of these ideas, we derive ...
متن کاملThe Sharp Form of the Strong Szegő Theorem
Let f be a function on the unit circle and Dn(f) be the determinant of the (n + 1) × (n + 1) matrix with elements {cj−i}0≤i,j≤n where cm = f̂m ≡ ∫ e−imθf(θ) dθ 2π . The sharp form of the strong Szegő theorem says that for any real-valued L on the unit circle with L, e in L( dθ 2π ), we have lim n→∞ Dn(eL)e−(n+1)L̂0 = exp ( ∞ ∑
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ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 2007
ISSN: 0894-9840,1572-9230
DOI: 10.1007/s10959-007-0060-7