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020 _a9783031737374
_9978-3-031-73737-4
024 7 _a10.1007/978-3-031-73737-4
_2doi
050 4 _aQA403-403.3
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKD
_2thema
100 1 _aCórdoba, Antonio.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_987174
245 1 0 _aSuprematism in Harmonic Analysis
_h[electronic resource] /
_cby Antonio Córdoba.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Birkhäuser,
_c2024.
300 _aXXII, 259 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematics,
_x2296-505X ;
_v356
505 0 _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.
520 _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.
650 0 _aHarmonic analysis.
_972301
650 0 _aFunctions of real variables.
_983964
650 0 _aFourier analysis.
650 1 4 _aAbstract Harmonic Analysis.
_972305
650 2 4 _aReal Functions.
_983965
650 2 4 _aFourier Analysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031737367
776 0 8 _iPrinted edition:
_z9783031737381
776 0 8 _iPrinted edition:
_z9783031737398
830 0 _aProgress in Mathematics,
_x2296-505X ;
_v356
_974786
856 4 0 _uhttps://doi.org/10.1007/978-3-031-73737-4
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c64790
_d64790