Summability of Multi-Dimensional Fourier Series and Hardy Spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2002
|
| Schriftenreihe: | Mathematics and Its Applications
541 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The history of martingale theory goes back to the early fifties when Doob [57] pointed out the connection between martingales and analytic functions. On the basis of Burkholder's scientific achievements the mar tingale theory can perfectly well be applied in complex analysis and in the theory of classical Hardy spaces. This connection is the main point of Durrett's book [60]. The martingale theory can also be well applied in stochastics and mathematical finance. The theories of the one-parameter martingale and the classical Hardy spaces are discussed exhaustively in the literature (see Garsia [83], Neveu [138], Dellacherie and Meyer [54, 55], Long [124], Weisz [216] and Duren [59], Stein [193, 194], Stein and Weiss [192], Lu [125], Uchiyama [205]). The theory of more-parameter martingales and martingale Hardy spaces is investigated in Imkeller [107] and Weisz [216]. This is the first mono graph which considers the theory of more-parameter classical Hardy spaces. The methods of proofs for one and several parameters are en tirely different; in most cases the theorems stated for several parameters are much more difficult to verify. The so-called atomic decomposition method that can be applied both in the one-and more-parameter cases, was considered for martingales by the author in [216] |
| Beschreibung: | 1 Online-Ressource (XV, 332 p) |
| ISBN: | 9789401731836 9789048159925 |
| DOI: | 10.1007/978-94-017-3183-6 |
Internformat
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| 500 | |a The history of martingale theory goes back to the early fifties when Doob [57] pointed out the connection between martingales and analytic functions. On the basis of Burkholder's scientific achievements the mar tingale theory can perfectly well be applied in complex analysis and in the theory of classical Hardy spaces. This connection is the main point of Durrett's book [60]. The martingale theory can also be well applied in stochastics and mathematical finance. The theories of the one-parameter martingale and the classical Hardy spaces are discussed exhaustively in the literature (see Garsia [83], Neveu [138], Dellacherie and Meyer [54, 55], Long [124], Weisz [216] and Duren [59], Stein [193, 194], Stein and Weiss [192], Lu [125], Uchiyama [205]). The theory of more-parameter martingales and martingale Hardy spaces is investigated in Imkeller [107] and Weisz [216]. This is the first mono graph which considers the theory of more-parameter classical Hardy spaces. The methods of proofs for one and several parameters are en tirely different; in most cases the theorems stated for several parameters are much more difficult to verify. The so-called atomic decomposition method that can be applied both in the one-and more-parameter cases, was considered for martingales by the author in [216] | ||
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| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401731836 9789048159925 |
| language | English |
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| spelling | Weisz, Ferenc Verfasser aut Summability of Multi-Dimensional Fourier Series and Hardy Spaces by Ferenc Weisz Dordrecht Springer Netherlands 2002 1 Online-Ressource (XV, 332 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 541 The history of martingale theory goes back to the early fifties when Doob [57] pointed out the connection between martingales and analytic functions. On the basis of Burkholder's scientific achievements the mar tingale theory can perfectly well be applied in complex analysis and in the theory of classical Hardy spaces. This connection is the main point of Durrett's book [60]. The martingale theory can also be well applied in stochastics and mathematical finance. The theories of the one-parameter martingale and the classical Hardy spaces are discussed exhaustively in the literature (see Garsia [83], Neveu [138], Dellacherie and Meyer [54, 55], Long [124], Weisz [216] and Duren [59], Stein [193, 194], Stein and Weiss [192], Lu [125], Uchiyama [205]). The theory of more-parameter martingales and martingale Hardy spaces is investigated in Imkeller [107] and Weisz [216]. This is the first mono graph which considers the theory of more-parameter classical Hardy spaces. The methods of proofs for one and several parameters are en tirely different; in most cases the theorems stated for several parameters are much more difficult to verify. The so-called atomic decomposition method that can be applied both in the one-and more-parameter cases, was considered for martingales by the author in [216] Mathematics Fourier analysis Sequences (Mathematics) Differential equations, partial Distribution (Probability theory) Fourier Analysis Approximations and Expansions Sequences, Series, Summability Probability Theory and Stochastic Processes Several Complex Variables and Analytic Spaces Mathematik Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Summierbarkeit (DE-588)4294383-8 gnd rswk-swf Hardy-Raum (DE-588)4159109-4 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 s Hardy-Raum (DE-588)4159109-4 s Summierbarkeit (DE-588)4294383-8 s 1\p DE-604 https://doi.org/10.1007/978-94-017-3183-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Weisz, Ferenc Summability of Multi-Dimensional Fourier Series and Hardy Spaces Mathematics Fourier analysis Sequences (Mathematics) Differential equations, partial Distribution (Probability theory) Fourier Analysis Approximations and Expansions Sequences, Series, Summability Probability Theory and Stochastic Processes Several Complex Variables and Analytic Spaces Mathematik Fourier-Reihe (DE-588)4155109-6 gnd Summierbarkeit (DE-588)4294383-8 gnd Hardy-Raum (DE-588)4159109-4 gnd |
| subject_GND | (DE-588)4155109-6 (DE-588)4294383-8 (DE-588)4159109-4 |
| title | Summability of Multi-Dimensional Fourier Series and Hardy Spaces |
| title_auth | Summability of Multi-Dimensional Fourier Series and Hardy Spaces |
| title_exact_search | Summability of Multi-Dimensional Fourier Series and Hardy Spaces |
| title_full | Summability of Multi-Dimensional Fourier Series and Hardy Spaces by Ferenc Weisz |
| title_fullStr | Summability of Multi-Dimensional Fourier Series and Hardy Spaces by Ferenc Weisz |
| title_full_unstemmed | Summability of Multi-Dimensional Fourier Series and Hardy Spaces by Ferenc Weisz |
| title_short | Summability of Multi-Dimensional Fourier Series and Hardy Spaces |
| title_sort | summability of multi dimensional fourier series and hardy spaces |
| topic | Mathematics Fourier analysis Sequences (Mathematics) Differential equations, partial Distribution (Probability theory) Fourier Analysis Approximations and Expansions Sequences, Series, Summability Probability Theory and Stochastic Processes Several Complex Variables and Analytic Spaces Mathematik Fourier-Reihe (DE-588)4155109-6 gnd Summierbarkeit (DE-588)4294383-8 gnd Hardy-Raum (DE-588)4159109-4 gnd |
| topic_facet | Mathematics Fourier analysis Sequences (Mathematics) Differential equations, partial Distribution (Probability theory) Fourier Analysis Approximations and Expansions Sequences, Series, Summability Probability Theory and Stochastic Processes Several Complex Variables and Analytic Spaces Mathematik Fourier-Reihe Summierbarkeit Hardy-Raum |
| url | https://doi.org/10.1007/978-94-017-3183-6 |
| work_keys_str_mv | AT weiszferenc summabilityofmultidimensionalfourierseriesandhardyspaces |