Professor Shapiro was an expert on trigonometric series and differential equations. He was internationally recognized for having solved a number of difficult problems in analysis [see the introduction to Contemporary Mathematics, Vol. 208, Editors: Michel L. Lapidus (coordinating editor); Lawrence H. Harper, Adolfo J. Rumbos]. He held academic positions at Rutgers University (1952-1960), the University of Oregon (1960-1964), and he spent three years at the Institute for Advanced Study. He joined UCR in 1964, where he worked for 46 years until his retirement in 2010. He published more than 100 papers during his long and productive career, and he was named a Fellow of the American Association for the Advancement of Science in 2003. In 2012, he was named a Fellow of the American Mathematical Society.
Professor Shapiro was very active even late in life-His book "Fourier Series in Several Variables with Applications to Partial Differential Equations" was published in 2011, when he was 86. He made outstanding contributions not only to research in mathematics, but also to the exposition of mathematics, teaching, and mentorship. In 1964, the National Science foundation awarded Professor Shapiro for his expository paper Fourier Series in Several Variables that appeared in the Bulletin of the American Mathematical Society. He supervised 20 doctoral students in his career.
At the time of his death in 2013, Professor Shapiro was survived by his wife, Florence, to whom he was happily married for nearly 65 years. He was also survived by four children, thirteen grandchildren, and a brother and sister.