Some comments on POLYNOMIALS and POLYNOMIAL INEQUALITIES:

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"...one of the best mathematical books in years"

"I found the original material particularly enjoyable"

Jet Wimp, Mathematical Intelligencer, (18) 1996, 78-79.

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"(the) presententation is very appealing..."

"This is a wonderful book..."

Walter Van Assche, SIAM Review, 38 (1996), 705-706.

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Review by D. S. Lubinsky in Math Reviews (97e:41001)

Congratulations to the authors on producing an excellent companion to G. Polya and G. Szego's classic Problems and theorems in analysis [Vol. I, English translation, Springer, New York, 1972; MR 49 #8782; Vol. II, 1976; MR 57 #5529]. As the title suggests, its focus is narrower than that of Polya and Szego, concentrating on polynomials, rational functions, trigonometric polynomials, and Muntz polynomials/rational functions, but its lively tutorial style makes it a delight to read. It highlights not only the authors' recent exciting results, but also many recent works that have not been surveyed anywhere in book form, while not neglecting the classics. Chebyshev, Remez, Bernstein, Cartan, Markov, Erdos, Turan, among others, are all represented, all with new twists, as are sharp inequalities for derivatives of polynomials, trigonometric polynomials, Muntz polynomials, rationals with pre-assigned poles, polynomials with zeros in some region, etc. There are delightful applications such as the length of a lemniscate, density of weighted polynomials, incomplete polynomials, irrationality and transcendence, etc.

This reviewer will make sure to have two copies; one for reference at work, and another at home to browse, and for bedtime/recreational reading, on the shelf next to Polya and Szego. For those analysts who do not have polynomials on their minds, the book will be a wonderful source of useful inequalities, results and extensive references.