منابع مشابه
Boundary Values of Bounded Holomorphic Functions of Several Variables
A typical result (consequence of Theorem 1) is that if such a function tends to a limit X as x—»x° from inside an open cone with vertex at x°, then it tends "on the average" to X as x—>x° from inside any open cone with vertex at x°. In particular, if such a function tends to limits in each of two open cones with a common vertex, these limits must be equal; for n = l (when the cones are half-lin...
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Let B(G) = {X : X ∈ Rn×n,X = X , I ≤ X ≤ I + A(G)} and C(G) = {X : X ∈ Rn×n,X = X , I − A(G) ≤ X ≤ I + A(G)} be classes of matrices associated with graph G. Here n is the number of vertices in graph G, and A(G) is the adjacency matrix of this graph. Denote r(G) = minX∈C(G) rank(X), r+(G) = minX∈B(G) rank(X). We have shown previously that for every graph G, α(G) ≤ r+(G) ≤ χ(G) holds and α(G) = r...
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Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$ are nonzero matrices and each $X_{i}$ is positive semidefinite. It is shown that if $f$ is a nonnegative increasing convex function on $left[ 0,infty right) $ satisfying $fleft( 0right) =0 $, then $$2s_{j}left( fleft( fra...
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We consider edge colourings of K n – the complete r-uniform hypergraph on n vertices. Our main question is: how ‘colourful’ can such a colouring be if we restrict the number of colours locally? The local restriction is formulated as follows: for a fixed hypergraph H and an integer k we call a colouring (H, k)-local, if every copy of H in the complete hypergraph K n picks up at most k different ...
متن کاملDistribution of values of bounded generalized polynomials
A generalized polynomial is a real-valued function which is obtained from conventional polynomials by the use of the operations of addition, multiplication, and taking the integer part; a generalized polynomial mapping is a vectorvalued mapping whose coordinates are generalized polynomials. We show that any bounded generalized polynomial mapping u:Z −→ R has a representation u(n) = f(φ(n)x), n ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2019
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14402