WEKO3
アイテム
{"_buckets": {"deposit": "376f6a0d-56fa-4f18-a84b-d84cf7f6fb05"}, "_deposit": {"id": "49244", "owners": [], "pid": {"revision_id": 0, "type": "depid", "value": "49244"}, "status": "published"}, "_oai": {"id": "oai:repository.dl.itc.u-tokyo.ac.jp:00049244", "sets": ["7722", "7725"]}, "item_4_biblio_info_7": {"attribute_name": "書誌情報", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "2016-10-31", "bibliographicIssueDateType": "Issued"}, "bibliographicIssueNumber": "4", "bibliographicPageEnd": "740", "bibliographicPageStart": "727", "bibliographicVolumeNumber": "23", "bibliographic_titles": [{"bibliographic_title": "Journal of Mathematical Sciences, The University of Tokyo"}]}]}, "item_4_description_5": {"attribute_name": "抄録", "attribute_value_mlt": [{"subitem_description": "For a Lebesgue integrable complex-valued function $f$ defined over the $m$-dimensional torus $\\mathbb {I}^m:=[0,1)^m$, let $\\hat f({\\bf n})$ denote the multiple Walsh-Fourier coefficient of $f$, where ${\\bf n}=\\left(n^{(1)},\\dots,n^{(m)}\\right)\\in (\\mathbb {Z}^+)^m$, $\\mathbb {Z^+}=\\mathbb {N}\\cup \\{0\\}$. The Riemann-Lebesgue lemma shows that $\\hat f({\\bf n})=o(1)$ as $|{\\bf n}|\\to \\infty$ for any $f\\in {\\rm L}^1(\\mathbb I^m)$. However, it is known that, these Fourier coefficients can tend to zero as slowly as we wish. The definitive result is due to Ghodadra Bhikha Lila for functions of bounded $p$-variation. We shall prove that this is just a matter only of local bounded $p$-variation for functions with multiple Walsh-Fourier series lacunary with small gaps. Our results, as in the case of trigonometric For a Lebesgue integrable complex-valued function $f$ defined over the $m$-dimensional torus $\\mathbb {I}^m:=[0,1)^m$, let $\\hat f({\\bf n})$ denote the multiple Walsh-Fourier coefficient of $f$, where ${\\bf n}=\\left(n^{(1)},\\dots,n^{(m)}\\right)\\in (\\mathbb {Z}^+)^m$, $\\mathbb {Z^+}=\\mathbb {N}\\cup \\{0\\}$. The Riemann-Lebesgue lemma shows that $\\hat f({\\bf n})=o(1)$ as $|{\\bf n}|\\to \\infty$ for any $f\\in {\\rm L}^1(\\mathbb I^m)$. However, it is known that, these Fourier coefficients can tend to zero as slowly as we wish. The definitive result is due to Ghodadra Bhikha Lila for functions of bounded $p$-variation. We shall prove that this is just a matter only of local bounded $p$-variation for functions with multiple Walsh-Fourier series lacunary with small gaps. Our results, as in the case of trigonometric Fourier series due to J.R. Patadia and R.G. Vyas, illustrate the interconnection between `localness\u0027 of the hypothesis and `type of lacunarity\u0027 and allow us to interpolate the results.", "subitem_description_type": "Abstract"}]}, "item_4_publisher_20": {"attribute_name": "出版者", "attribute_value_mlt": [{"subitem_publisher": "Graduate School of Mathematical Sciences, The University of Tokyo"}]}, "item_4_select_14": {"attribute_name": "著者版フラグ", "attribute_value_mlt": [{"subitem_select_item": "publisher"}]}, "item_4_source_id_10": {"attribute_name": "書誌レコードID", "attribute_value_mlt": [{"subitem_source_identifier": "AA11021653", "subitem_source_identifier_type": "NCID"}]}, "item_4_source_id_8": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "13405705", "subitem_source_identifier_type": "ISSN"}]}, "item_4_text_17": {"attribute_name": "Mathmatical Subject Classification", "attribute_value_mlt": [{"subitem_text_value": "42C10(MSC2010)"}, {"subitem_text_value": "42B05(MSC2010)"}, {"subitem_text_value": "26B30(MSC2010)"}, {"subitem_text_value": " 26D15(MSC2010)"}]}, "item_4_text_33": {"attribute_name": "原稿受領日", "attribute_value_mlt": [{"subitem_text_value": "2014-11-17"}]}, "item_4_text_4": {"attribute_name": "著者所属", "attribute_value_mlt": [{"subitem_text_value": "Department of Mathematics, Faculty of Science, The M. S. University of Baroda"}]}, "item_creator": {"attribute_name": "著者", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Ghodadra, Bhikha Lila"}], "nameIdentifiers": [{"nameIdentifier": "146120", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "ファイル情報", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2018-04-04"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "jms230401.pdf", "filesize": [{"value": "146.0 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 146000.0, "url": {"label": "jms230401.pdf", "url": "https://repository.dl.itc.u-tokyo.ac.jp/record/49244/files/jms230401.pdf"}, "version_id": "470725c9-73aa-429d-b6d5-a5ac63c5af8a"}]}, "item_keyword": {"attribute_name": "キーワード", "attribute_value_mlt": [{"subitem_subject": "Multiple Walsh-Fourier coefficient ", "subitem_subject_scheme": "Other"}, {"subitem_subject": " Function of bounded p-variation in several variables ", "subitem_subject_scheme": "Other"}, {"subitem_subject": " order of magnitude ", "subitem_subject_scheme": "Other"}, {"subitem_subject": " Lacunary Fourier series with small gaps", "subitem_subject_scheme": "Other"}]}, "item_language": {"attribute_name": "言語", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"resourcetype": "departmental bulletin paper", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "On the Coefficients of Multiple Walsh-Fourier Series with Small Gaps", "item_titles": {"attribute_name": "タイトル", "attribute_value_mlt": [{"subitem_title": "On the Coefficients of Multiple Walsh-Fourier Series with Small Gaps"}]}, "item_type_id": "4", "owner": "1", "path": ["7722", "7725"], "permalink_uri": "http://hdl.handle.net/2261/00074368", "pubdate": {"attribute_name": "公開日", "attribute_value": "2018-04-04"}, "publish_date": "2018-04-04", "publish_status": "0", "recid": "49244", "relation": {}, "relation_version_is_last": true, "title": ["On the Coefficients of Multiple Walsh-Fourier Series with Small Gaps"], "weko_shared_id": null}
On the Coefficients of Multiple Walsh-Fourier Series with Small Gaps
http://hdl.handle.net/2261/00074368
http://hdl.handle.net/2261/000743688a499b33-a37c-4127-b235-6982e1e74d0b
名前 / ファイル | ライセンス | アクション |
---|---|---|
jms230401.pdf (146.0 kB)
|
|
Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
---|---|---|---|---|---|---|
公開日 | 2018-04-04 | |||||
タイトル | ||||||
タイトル | On the Coefficients of Multiple Walsh-Fourier Series with Small Gaps | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
主題 | Multiple Walsh-Fourier coefficient | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | Function of bounded p-variation in several variables | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | order of magnitude | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | Lacunary Fourier series with small gaps | |||||
主題Scheme | Other | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
著者 |
Ghodadra, Bhikha Lila
× Ghodadra, Bhikha Lila |
|||||
著者所属 | ||||||
著者所属 | Department of Mathematics, Faculty of Science, The M. S. University of Baroda | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | For a Lebesgue integrable complex-valued function $f$ defined over the $m$-dimensional torus $\mathbb {I}^m:=[0,1)^m$, let $\hat f({\bf n})$ denote the multiple Walsh-Fourier coefficient of $f$, where ${\bf n}=\left(n^{(1)},\dots,n^{(m)}\right)\in (\mathbb {Z}^+)^m$, $\mathbb {Z^+}=\mathbb {N}\cup \{0\}$. The Riemann-Lebesgue lemma shows that $\hat f({\bf n})=o(1)$ as $|{\bf n}|\to \infty$ for any $f\in {\rm L}^1(\mathbb I^m)$. However, it is known that, these Fourier coefficients can tend to zero as slowly as we wish. The definitive result is due to Ghodadra Bhikha Lila for functions of bounded $p$-variation. We shall prove that this is just a matter only of local bounded $p$-variation for functions with multiple Walsh-Fourier series lacunary with small gaps. Our results, as in the case of trigonometric For a Lebesgue integrable complex-valued function $f$ defined over the $m$-dimensional torus $\mathbb {I}^m:=[0,1)^m$, let $\hat f({\bf n})$ denote the multiple Walsh-Fourier coefficient of $f$, where ${\bf n}=\left(n^{(1)},\dots,n^{(m)}\right)\in (\mathbb {Z}^+)^m$, $\mathbb {Z^+}=\mathbb {N}\cup \{0\}$. The Riemann-Lebesgue lemma shows that $\hat f({\bf n})=o(1)$ as $|{\bf n}|\to \infty$ for any $f\in {\rm L}^1(\mathbb I^m)$. However, it is known that, these Fourier coefficients can tend to zero as slowly as we wish. The definitive result is due to Ghodadra Bhikha Lila for functions of bounded $p$-variation. We shall prove that this is just a matter only of local bounded $p$-variation for functions with multiple Walsh-Fourier series lacunary with small gaps. Our results, as in the case of trigonometric Fourier series due to J.R. Patadia and R.G. Vyas, illustrate the interconnection between `localness' of the hypothesis and `type of lacunarity' and allow us to interpolate the results. | |||||
書誌情報 |
Journal of Mathematical Sciences, The University of Tokyo 巻 23, 号 4, p. 727-740, 発行日 2016-10-31 |
|||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 13405705 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA11021653 | |||||
著者版フラグ | ||||||
値 | publisher | |||||
Mathmatical Subject Classification | ||||||
42C10(MSC2010) | ||||||
Mathmatical Subject Classification | ||||||
42B05(MSC2010) | ||||||
Mathmatical Subject Classification | ||||||
26B30(MSC2010) | ||||||
Mathmatical Subject Classification | ||||||
26D15(MSC2010) | ||||||
出版者 | ||||||
出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
原稿受領日 | ||||||
2014-11-17 |