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This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression.In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of whichFourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory. Autorid: Elias M. Stein, Rami Shakarchi

WINNER OF THE 2025 PULITZER PRIZE Winner of the Pushkin House Russian Book Prize Shortlisted for the Cundill History Prize A "riveting history" (Wall Street Journal) of the Soviet dissident movement, which hastened the end of the USSR and still provides a model of opposition in Putins Russiaand beyond A book about a past time that is very much a book for our time. . . . A story from which we all stand to learn as we face a new wave of authoritarianism.Los Angeles Review of Books Beginning in the 1960s, the Soviet Union was unexpectedly confronted by a dissident movement that captured the worlds imagination. Demanding that the Kremlin obey its own laws, an improbable band of Soviet citizens held unauthorized public gatherings, petitioned in support of arrested intellectuals, and circulated banned samizdat texts. Soviet authorities arrested dissidents, subjected them to bogus trials and vicious press campaigns, sentenced them to psychiatric hospitals and labor camps, sent them into exileand transformed them into martyred heroes. Against all odds, the dissident movement undermined the Soviet system and hastened its collapse. Taking its title from a toast made at dissident gatherings, To the Success of Our Hopeless Cause is a definitive history of a remarkable group of people who helped change the twentieth century. Benjamin Nathanss vivid narrative tells the dramatic story of the men and women who became dissidentsfrom Nobel laureates Andrei Sakharov and Alexander Solzhenitsyn to many others who are virtually unknown today. Drawing on diaries, memoirs, personal letters, interviews, and KGB interrogation records, To the Success of Our Hopeless Cause reveals how dissidents decided to use Soviet law to contain the power of the Soviet state. This strategy, as one of them put it, was simple to the point of genius: in an unfree country, they began to conduct themselves like free people. An extraordinary account of the Soviet dissident movement, To the Success of Our Hopeless Cause shows how dissidents spearheaded the struggle to break free of the USSRs totalitarian past, a struggle that continues in Putins Russiaand that illuminates other struggles between hopelessness and perseverance today. Autorid: Benjamin Nathans

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