On sums of projections
نویسندگان
چکیده
منابع مشابه
Semi-continuity of Metric Projections in ∞-direct Sums
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15 صفحه اولOn Sums of Dilates
Let k be a positive integer and let A ⊂ Z. We let k · A = {ka : a ∈ A} denote the k-dilation of A, and let kA = A+ · · ·+ A (k-times) be the k-fold sumset of A. We observe that A+ k · A ⊂ A+ kA = (k + 1)A and that, in general, A+ k · A is much smaller than (k + 1)A. It is well known that |(k + 1)A| (k + 1)|A| − k, and that equality holds only if A is an arithmetic progression. Indeed, if A is a...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1969
ISSN: 0022-1236
DOI: 10.1016/0022-1236(69)90027-5