Fourier analysis of economic phenomena:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore
Springer
[2018]
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| Series: | Monographs in mathematical economics
Volume 2 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | xi, 410 Seiten Illustrationen 23.5 cm x 15.5 cm |
| ISBN: | 9789811327292 |
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MARC
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| 245 | 1 | 0 | |a Fourier analysis of economic phenomena |c Toru Maruyama |
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| 653 | |a Bochner Theorem | ||
| 653 | |a Fourier analysis | ||
| 653 | |a Kaldor-Kalecki theory | ||
| 653 | |a Slutsky effect | ||
| 653 | |a business cycle | ||
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Record in the Search Index
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| adam_text | Contents 1 Fourier Series on Hilbert Spaces..................................................................... 1.1 Hilbert Spaces........................................................................................... 1.2 Orthonormal Systems............................................................................... 1.3 Fourier Series............................................................................................ 1.4 Completeness of Orthonormal Systems............................................. References................................................................................................................. 1 1 5 11 14 21 2 Convergence of Classical Fourier Series...................................................... 2.1 Dirichlet Integrals...................................................................................... 2.2 Dini, Jordan Tests.................................................................................... 2.3 Almost Everywhere Convergence: Historical Survey.................... 2.4 Uniform Convergence............................................................................ 2.5 Fejér Integral and (C, l)-summability............................................... References................................................................................................................. 23 24 28 34 37 40 44 3 Fourier Transforms (I)........................................................................................ 3.1 Fourier
Integrals........................................................................................ 3.2 Fourier Transforms on İÎ1 (R, C)......................................................... 47 47 52 3.3 Application: Heat Equation................................................................... References................................................................................................................. 60 62 Fourier Transforms (II)...................................................................................... 4.1 Fourier Transforms of Rapidly Decreasing Functions................... 4.2 Fourier Transforms on Ü2(R, C) ......................................................... 65 65 72 4.3 4.4 4.5 Application: Integral Equations of Convolution Type.................... Fourier Transforms of Tempered Distributions................................ Fourier Transforms on ii2(R, C) Revisited....................................... 75 78 87 4.6 Periodic Distributions............................................................................. References................................................................................................................. 92 99 Summability Kernels and SpectralSynthesis ............................................. 5.1 Shift Operators......................................................................................... 5.2 Summability Kernels on [—π, π]........................................................ 101 101 105 4 5 ix
Contents 5.3 Spectral Synthesis on [—π, π] ....................................................... 109 5.4 Summability Kernels on R............................................................. Ill 5.5 Spectral Synthesis on R: Inverse Fourier Transforms on fi1........ 115 References..................................................................................................... 119 Fourier Transforms of Measures.............................................................. 6.1 Radon Measures ............................................................................. 6.2 Fourier Coefficients of Measures ( 1 ).............................................. 6.3 Fourier Coefficients of Measures (2).............................................. 6.4 Herglotz’s Theorem......................................................................... 6.5 Fourier Transforms of Measures................................................... 6.6 Bochner’s Theorem......................................................................... 6.7 Convolutions of Measures.............................................................. 6.8 Wiener’s Theorem.......................................................................... References..................................................................................................... 121 121 122 126 129 136 146 154 158 163 Spectral Representation of Unitary Operators...................................... 7.1 Lax-Milgram Theorem.................................................................. 7.2 Conjugate Operators and
Projections............................................ 7.3 Unitary Operators............................................................................ 7.4 Resolution of the Identity............................................................... 7.5 Spectral Representation of Unitary Operators.............................. 7.6 Stone’s Theorem............................................................................. References..................................................................................................... 165 165 169 175 177 180 187 191 Periodic Weakly Stationary Processes..................................................... 8.1 Stochastic Processes of Second Order.......................................... 8.2 Weakly Stationary Stochastic Processes....................................... 8.3 Periodicity of Weakly Stationary Stochastic Process .................. 8.4 Orthogonal Measures..................................................................... 8.5 Spectral Representation of Weakly Stationary Processes............ 8.6 Spectral Density Functions............................................................ 8.7 A Note on Slutsky’s Work 6437180 References..................................................................................................... 193 194 200 210 216 221 227 238 243 Almost Periodic Functions and Stochastic Processes........................... 9.1 Almost Periodic Functions............................................................ 9.2 Щ5 (R, €) as a Closed Subalgebra of P°°(R, C)........................... 9.3 Spectrum of
Almost Periodic Functions....................................... 9.4 Fourier Series of Almost Periodic Functions................................ 9.5 Almost Periodic Weakly Stationary Stochastic Processes........... References..................................................................................................... 245 245 247 256 266 274 277 Fredholm Operators .................................................................................. 10.1 Direct Sums and Projections.......................................................... 10.2 Fredholm Operators: Definitions and Examples........................... 10.3 Parametrix........................................................................................ 279 279 290 293
Contents xi 10.4 Product of Fredholm Operators..................................................... 295 10.5 Stability of Indices.......................................................................... 298 References..................................................................................................... 299 11 Hopf Bifurcation Theorem....................................................................... 11.1 Ljapunov-Schmidt Reduction Method......................................... 11.2 Abstract Hopf Bifurcation Theorem.............................................. 11.3 Classical Hopf Bifurcation for Ordinary Differential Equations . 11.4 Smoothness of F............................................................................. 11.5 dim® =2....................................................................................... 11.6 codim 31 = 2................................................................................... 11.7 Linear Independence of PMv* and PNv* (1)............................. 11.8 Linear Independence of PMv* and PNv* (2)............................. 11.9 Hopf Bifurcation in G7..................................................................... 11.10 Kaldorian Business Fluctuations................................................... 11.11 Ljapunov’s Center Theorem........................................................... References..................................................................................................... 301 303 305 309 312 315 317 321 322 328 330 335 344 Appendix A Exponential Function
еІѲ........................................................ A.l Complex Exponential Function...................................................... A.2 Imaginary Exponential Function.................................................... A.3 Torus Κ/2πΖ.................................................................................... A.4 A Homomorphism of R into U....................................................... A.5 Functions and σ -Fields on the Toms.............................................. References..................................................................................................... 347 347 349 352 354 355 356 Appendix В Topics from Functional Analysis............................................ B.l Inductive Limit Topology................................................................ B.2 Duals of Locally Convex Spaces.................................................... References..................................................................................................... 357 357 366 377 AppendixC Theory of Distributions........................................................... C.l The Space T ..................................................................................... C.2 Examples of Test Functions and an Approximation Theorem .... C.3 Distributions: Definition and Examples.......................................... C.4 Differentiation of Distributions ...................................................... C.5 Topologies on the Space £ (£?) of Distributions...........................
References..................................................................................................... 379 379 384 388 392 396 402 Addendum........................................................................................................... 403 References..................................................................................................... 404 Name Index.......................................................................................................... 405 Subject Index 407
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| any_adam_object | 1 |
| author | Maruyama, Tōru |
| author_GND | (DE-588)114496838 |
| author_facet | Maruyama, Tōru |
| author_role | aut |
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| author_variant | t m tm |
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| bvnumber | BV046079805 |
| classification_rvk | QC 330 SK 450 |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| isbn | 9789811327292 |
| language | English |
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| spelling | Maruyama, Tōru Verfasser (DE-588)114496838 aut Fourier analysis of economic phenomena Toru Maruyama Singapore Springer [2018] © 2018 xi, 410 Seiten Illustrationen 23.5 cm x 15.5 cm txt rdacontent n rdamedia nc rdacarrier Monographs in mathematical economics Volume 2 Dynamisches Modell (DE-588)4150932-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Konjunkturzyklus (DE-588)4032134-4 gnd rswk-swf Wirtschaftstheorie (DE-588)4079351-5 gnd rswk-swf Bochner Theorem Fourier analysis Kaldor-Kalecki theory Slutsky effect business cycle Harmonische Analyse (DE-588)4023453-8 s Wirtschaftstheorie (DE-588)4079351-5 s Dynamisches Modell (DE-588)4150932-8 s Konjunkturzyklus (DE-588)4032134-4 s b DE-604 Erscheint auch als Online-Ausgabe 978-981-13-2730-8 Monographs in mathematical economics Volume 2 (DE-604)BV042917126 2 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=0419cedd2a9640d3a17440f670c85133&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031460927&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Maruyama, Tōru Fourier analysis of economic phenomena Monographs in mathematical economics Dynamisches Modell (DE-588)4150932-8 gnd Harmonische Analyse (DE-588)4023453-8 gnd Konjunkturzyklus (DE-588)4032134-4 gnd Wirtschaftstheorie (DE-588)4079351-5 gnd |
| subject_GND | (DE-588)4150932-8 (DE-588)4023453-8 (DE-588)4032134-4 (DE-588)4079351-5 |
| title | Fourier analysis of economic phenomena |
| title_auth | Fourier analysis of economic phenomena |
| title_exact_search | Fourier analysis of economic phenomena |
| title_full | Fourier analysis of economic phenomena Toru Maruyama |
| title_fullStr | Fourier analysis of economic phenomena Toru Maruyama |
| title_full_unstemmed | Fourier analysis of economic phenomena Toru Maruyama |
| title_short | Fourier analysis of economic phenomena |
| title_sort | fourier analysis of economic phenomena |
| topic | Dynamisches Modell (DE-588)4150932-8 gnd Harmonische Analyse (DE-588)4023453-8 gnd Konjunkturzyklus (DE-588)4032134-4 gnd Wirtschaftstheorie (DE-588)4079351-5 gnd |
| topic_facet | Dynamisches Modell Harmonische Analyse Konjunkturzyklus Wirtschaftstheorie |
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