Bounds for the average -extreme and the -extreme discrepancy.
Construction of minimal bracketing covers for rectangles.
Discrepancy of symmetric products of hypergraphs.
On -discrepancy and mixed Monte Carlo and quasi-Monte Carlo sequences.
Differentiable -functional calculus for certain sums of non-commuting operators
We consider a special class of sums of non-commuting positive operators on L²-spaces and derive a formula for their holomorphic semigroups. The formula enables us to give sufficient conditions for these operators to admit differentiable -functional calculus for 1 ≤ p ≤ ∞. Our results are in particular applicable to certain sub-Laplacians, Schrödinger operators and sums of even powers of vector fields on solvable Lie groups with exponential volume growth.
Page 1