03414nam 2200625 450 991078875060332120170821171912.01-4704-0172-X(CKB)3360000000464771(EBL)3113775(SSID)ssj0000889303(PQKBManifestationID)11475770(PQKBTitleCode)TC0000889303(PQKBWorkID)10876524(PQKB)11664424(MiAaPQ)EBC3113775(RPAM)4944124(PPN)195414691(EXLCZ)99336000000046477120140902h19961996 uy 0engur|n|---|||||txtccrWavelet methods for pointwise regularity and local oscillations of functions /Stéphane Jaffard, Yves MeyerProvidence, Rhode Island :American Mathematical Society,1996.©19961 online resource (127 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 123, Number 587"September 1996, Volume 123, Number 587 (second of 4 numbers)."0-8218-0475-8 Includes bibliographical references and index.""Table of contents""; ""Introduction""; ""I. Modulus of continuity and two-microlocalization""; ""l.1 Modulus of continuity""; ""l.2 Pointwise smoothness and two-microlocalization""; ""l.3 Pseudodifferential operators and two-microlocalization""; ""l.4 Characterizations of two-microlocal spaces""; ""II. Singularities of functions in Sobolev spaces""; ""II.1 Hausdorff dimension of the singularities of functions in L[sup(p,s)]""; ""ll.2 Packing dimension of strong α-singularities""; ""ll.3 Singularities of BV functions""; ""ll.4 Sobolev regularity of trace functions""""III. Wavelets and lacunary trigonometric series""""lll.1 Pointwise regularity of Hardy functions""; ""lll.2 Convergence and derivability of wavelet series""; ""IV. Properties of chirp expansions""; ""IV.1 Indefinitely oscillating functions and chirps""; ""IV.2 Characterization of chirps: statement of results""; ""IV.3 Proof of Theorem 5.2: (I) â?? (II)""; ""IV.4 Proof of Theorem 5.2: (II) â?? (I)""; ""IV.5 Proof of Theorem 5.2: (I) â?? (III)""; ""V. Trigonometric chirps""; ""V.1 Definition and statement of the main theorem""; ""V.2 Some asymptotic expansions""; ""V.3 Proof of Theorem 5.1""""VI. Logarithmic chirps""""VII. The Riemann series""; ""VII.1 Trigonometric chirps at rationals""; ""VII.2 Logarithmic chirps at quadratic irrationals""; ""References""; ""Index""; ""Notations""Memoirs of the American Mathematical Society ;Volume 123, Number 587.Wavelets (Mathematics)Littlewood-Paley theoryMicrolocal analysisSignal processingMathematicsWavelets (Mathematics)Littlewood-Paley theory.Microlocal analysis.Signal processingMathematics.515/.84Jaffard Stéphane1962-422336Meyer YvesMiAaPQMiAaPQMiAaPQBOOK9910788750603321Wavelet methods for pointwise regularity and local oscillations of functions3759931UNINA