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Statement of the inequality. Suppose is a natural number and are positive numbers and: Then the Shapiro inequality states that. where and . For greater values of the inequality does not hold, and the strict lower bound is with . The initial proofs of the inequality in the pivotal cases [2] and [3] rely on numerical computations.
Joel H. Shapiro is an American mathematician, active in the field of composition operators. He is the author of the book Composition Operators and Classical Function Theory ( ISBN 3540940677 ), and the American Mathematical Society memoir "Cyclic Phenomena for Composition Operators" (Memoirs of the American Math.
Shapiro was born in Passaic, New Jersey in 1953 and was raised in Glen Rock, New Jersey. [1] In interviews, Shapiro has stated an early favorite band of his was The Beatles, but that he soon became a bigger fan of The Four Seasons when he noticed it had a dedicated keyboard player, Bob Gaudio, which the Beatles did not at the time. [1]
‘No one in the US should be retiring at 65’: Ben Shapiro says Social Security was not designed to provide retirement benefits for 20+ years — and those who expect that are ‘crazy’
Irwin Shapiro was born in Pittsburgh, Pennsylvania. [1] Little is known of his background or upbringing. His family probably came from what is now Hungary, since his first published books in the late 1930s are translations from Hungarian. Shapiro studied at the Art Students League in New York City, where he is known to have taken at least one ...
Shapiro was born on October 31, 1899, in New York City. [1] He became a Tin Pan Alley songwriter and accompanied notable star vaudeville singers of the day, including Nora Bayes and Eva Tanguay. [1] Shapiro was hired as accompanist and music director for Sophie Tucker; replacing the "Five Kings of Syncopation" on her 1922 tour to London. [2]