# boundedness

## Definitions

• WordNet 3.6
• n boundedness the quality of being finite
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Century Dictionary and Cyclopedia
• n boundedness The quality of being bounded, limited, or circumscribed; limited extent or range.
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## Usage

### In science:

Therefore πn (∆) = span {D(t, n) | t ∈ N} and hence condition 1◦ of [15, 2.1] follows from the boundedness of (22) as n → ∞.
Invariant subspaces of Voiculescu's circular operator
The boundedness of Ig (a) implies that we can ignore the ﬁrst few n for the price of increasing the constant C1 .
Fast graphs for the random walker
Thus we can apply Theorem 3.2, whereis the boundedness of the density of the invariant measures follows.
Perron-Frobenius spectrum for random maps and its approximation
Still, also in these examples without convergence of the mean, under the assumption of uniform boundedness of the distribution, selfaveraging in the sense of Theorem 1 would hold.
Universal bounds on the selfaveraging of random diffraction measures
The functor M 7→ T ⊗L B M is an equivalence D(Mod B ) → D(Mod A) preserving boundedness.
Dualizing Complexes and Tilting Complexes over Simple Rings
Eichhorn, The boundedness of connection coeﬃcients and their derivatives, Math.
Relative Zeta Functions, Determinants, Torsion, Index Theorems and Invariants for Open Manifolds
Nevertheless, there is a simple analytic criterion — the uniform boundedness of the energy of the map and the L2 norm of α — that ensures that the moduli space is compact.
Family Gromov-Witten Invariants for Kahler Surfaces
Except for the self-adjointness condition when we consider eigenvalues, the only assumptions on the distribution of the matrix entries are independence and boundedness.
Concentration of norms and eigenvalues of random matrices
We note that aside from the uniform boundedness assumption, the distributions of the independent entries of X in Theorems 1 and 2 are completely arbitrary.
Concentration of norms and eigenvalues of random matrices
Domar, Uniform boundedness in families related to subharmonic functions, J.
A generalized mean value inequality for subharmonic functions and applications
Boundedness of solutions to variational problems under general growth conditions.
Random Surfaces
In , boundedness of the absolute ﬁrst moment has been proved for d = 2, but no exponential decay of the correlations.
Localization-delocalization phenomena for random interfaces
In order to treat A(z ) and B (z ) in weighted L2 -spaces and weighted Sobolev spaces, we need terminology and a boundedness result on pseudodifferential operators in these spaces.
Generalized eigenfunctions of relativistic Schroedinger operators I
Actually, we shall obtain two suﬃcient conditions (see Lemmas 5.2 and 5.3 below), either of which is suitable for showing the boundedness of generalized eigenfunctions of √−∆ + V (x) on R3 .
Generalized eigenfunctions of relativistic Schroedinger operators I
On the other hand, we are going to show a few boundedness results on G0 in the framework of weighted L2 -spaces as well as in some other frameworks.
Generalized eigenfunctions of relativistic Schroedinger operators I
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