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Most of the " extremal problems " of Harmonic (or Fourier) Analysis which emerged before the year 2000 were actually born in the twentieth century, and their emergences were scattered throughout that century, including the two world war periods. A great many of these problems pertain to polynomials, trigonometric poly-nomials and (finite) exponential sums.(More)
Lipoprotein lipase (LPL) is an important enzyme in lipid metabolism, and adipose LPL activity is increased in rats that are deficient in thyroid hormone. To examine the mechanism of thyroid hormone's effect on LPL, LPL gene expression was assessed in the epididymal fat pads of hypothyroid rats. When compared to control rats, LPL activity, mass, and(More)
Patients with diabetes commonly manifest hypertriglyceridemia along with decreased adipose tissue lipoprotein lipase (LPL) activity, and improved diabetes control tends to reverse these abnormalities. To better understand the mechanism of regulation of LPL in diabetes, 11 diabetic patients (3 type I, 8 type II) were brought under improved glycemic control,(More)
Macrophages are important cells in the pathogenesis of atherosclerosis because of their tendency to accumulate lipid and become transformed into foam cells. Cultured human monocyte-derived macrophages spontaneously secrete lipoprotein lipase (LPL), and LPL has been linked to increased lipid uptake by these cells. Because secretion of various macrophage(More)
and statement of results 1.1. The object of this note is to answer (in the affirmative) the first two open problems stated at the end of a previous paper by one of us [5]. (For the sake of clarity we first reproduce here part of the introduction of [5], to which we refer for notation and more details.) 1.2. Let N (resp. N*) denote the set of all(More)
A sum of exponentials of the form f (x) = exp (2πiN 1 x)+exp (2πiN 2 x)+ · · · + exp (2πiN m x), where the N k are distinct integers is called an idempotent trigonometric polynomial (because the convolution of f with itself is f) or, simply, an idempotent. We show that for every p > 1, and every set E of the torus T = R/Z with |E| > 0, there are idempotents(More)
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