03606nam a22004575i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001600153072001700169072002300186072001600209100008100225245008500306250001800391264007300409300003500482336002600517337002600543338003600569347002400605490004700629505042900676520163001105650002302735650003302758650002202791650003202813650002002845650002202865710003402887773002602921776003602947776003602983776003603019830004703055856004603102978-3-031-73737-4DE-He21320251030113302.0cr nn 008mamaa241108s2024    sz |    s    |||| 0|eng d  a97830317373747 a10.1007/978-3-031-73737-42doi 4aQA403-403.3 7aPBKD2bicssc 7aMAT0340002bisacsh 7aPBKD2thema1 aCórdoba, Antonio.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aSuprematism in Harmonic Analysish[electronic resource] /cby Antonio Córdoba.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Birkhäuser,c2024.  aXXII, 259 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aProgress in Mathematics,x2296-505X ;v3560 aPreface -- Notions and terminology -- 1. Seven mathematical haikus -- 2. All those rectangles -- 3. As a needle turn: Besicovitch or Kakeya sets -- 4. Translation invariant operators -- 5. The multiplier problem for the ball -- 6. The ball multiplier on mixed norm spaces -- 7. The Poisson summation formula -- 8. Encounters at the interface with number theory -- 9. Weyl sums and atomic energy oscillations -- Bibliography.  aThis award-winning monograph explores advanced topics in harmonic analysis, addressing both classical and contemporary problems. Several connections to number theory, crystallography or atomic theory are also surveyed. The term “suprematism” refers to a certain geometric point of view underlying proofs and arguments. The opening of the book is dedicated to a few results, with short statements and proofs, that could be called “mathematical haikus”. Then, in the first part of the book, singular integrals beyond the classical Calderón-Zygmund theory, such as Vitali-type covering lemmas and estimates for the corresponding maximal operators, are explored. The exponential overlapping of parallelepipeds, the strong maximal function, and Zygmund's conjecture about monotonic bases are also covered. The core of this part is devoted to the Kakeya maximal function and its relation to the spherical summation of Fourier series and integrals. The two-dimensional case is well understood, but the case of higher dimensions still presents many open problems and conjectures. The chapters in the second part of the book treat questions at the interface of harmonic analysis and number theory, including applications of the Poisson summation formula to crystallography and arithmetic, estimates of the Minkowski dimension of Riemann graphs, random lattice point problems, and the role of Weyl sums in atomic energy oscillations. With a focus on rigorous research insights for graduate students and researchers in mathematics, this book provides a comprehensive journey through the hidden landscapes of harmonic analysis. 0aHarmonic analysis. 0aFunctions of real variables. 0aFourier analysis.14aAbstract Harmonic Analysis.24aReal Functions.24aFourier Analysis.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303173736708iPrinted edition:z978303173738108iPrinted edition:z9783031737398 0aProgress in Mathematics,x2296-505X ;v35640uhttps://doi.org/10.1007/978-3-031-73737-4