On the Riesz constants for systems of integer translates

In this paper, one-parameter families of integer translates of the Gaussian and Lorentz functions are studied. For a Lorentz function, we obtain formulas for the coefficients of the series defining node functions and show that the limit value of node functions is given by a sample function. For syst...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical Notes 2014-07, Vol.96 (1-2), p.228-238
Main Authors: Kiselev, E. A., Minin, L. A., Novikov, I. Ya, Sitnik, S. M.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c288t-bc9a1b6eafeab96ecdd0f1950f1651087ee20e9aeffafdb2be887dc838601e513
cites cdi_FETCH-LOGICAL-c288t-bc9a1b6eafeab96ecdd0f1950f1651087ee20e9aeffafdb2be887dc838601e513
container_end_page 238
container_issue 1-2
container_start_page 228
container_title Mathematical Notes
container_volume 96
creator Kiselev, E. A.
Minin, L. A.
Novikov, I. Ya
Sitnik, S. M.
description In this paper, one-parameter families of integer translates of the Gaussian and Lorentz functions are studied. For a Lorentz function, we obtain formulas for the coefficients of the series defining node functions and show that the limit value of node functions is given by a sample function. For systems of translates generated by the Gaussian and Lorentz functions as well as by the node functions related to them, we obtain explicit expressions for the Riesz constants and study the parameter-dependent behavior of these constants. While proving some of the results of this paper, we establish the monotonicity of a special ratio of two Jacobi theta functions, a fact which is of interest in itself.
doi_str_mv 10.1134/S0001434614070244
format article
fullrecord <record><control><sourceid>crossref_sprin</sourceid><recordid>TN_cdi_crossref_primary_10_1134_S0001434614070244</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1134_S0001434614070244</sourcerecordid><originalsourceid>FETCH-LOGICAL-c288t-bc9a1b6eafeab96ecdd0f1950f1651087ee20e9aeffafdb2be887dc838601e513</originalsourceid><addsrcrecordid>eNp9j91KxDAQhYMoWFcfwLu8QHWmTdP0UhZ_FhYW_LkuaTvRLrupZOLF-vSmrHeCNzMM55zhO0JcI9wglur2BQBQlUqjghoKpU5EhlVd5sbU-lRks5zP-rm4YN6mCzVCJszGy_hB8nkk_pb95DlaH1m6KUg-cKQ9y8nJ0Ud6pyBjsJ53NhJfijNnd0xXv3sh3h7uX5dP-XrzuFrerfO-MCbmXd9Y7DRZR7ZrNPXDAA6bKg1dIZiaqABqLDln3dAVHSXgoTel0YBUYbkQePzbh4k5kGs_w7i34dAitHP19k_1lCmOGU5en7jb7fQVfML8J_QDp-Zb3g</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On the Riesz constants for systems of integer translates</title><source>Springer Nature</source><creator>Kiselev, E. A. ; Minin, L. A. ; Novikov, I. Ya ; Sitnik, S. M.</creator><creatorcontrib>Kiselev, E. A. ; Minin, L. A. ; Novikov, I. Ya ; Sitnik, S. M.</creatorcontrib><description>In this paper, one-parameter families of integer translates of the Gaussian and Lorentz functions are studied. For a Lorentz function, we obtain formulas for the coefficients of the series defining node functions and show that the limit value of node functions is given by a sample function. For systems of translates generated by the Gaussian and Lorentz functions as well as by the node functions related to them, we obtain explicit expressions for the Riesz constants and study the parameter-dependent behavior of these constants. While proving some of the results of this paper, we establish the monotonicity of a special ratio of two Jacobi theta functions, a fact which is of interest in itself.</description><identifier>ISSN: 0001-4346</identifier><identifier>EISSN: 1573-8876</identifier><identifier>DOI: 10.1134/S0001434614070244</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Mathematics ; Mathematics and Statistics</subject><ispartof>Mathematical Notes, 2014-07, Vol.96 (1-2), p.228-238</ispartof><rights>Pleiades Publishing, Ltd. 2014</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c288t-bc9a1b6eafeab96ecdd0f1950f1651087ee20e9aeffafdb2be887dc838601e513</citedby><cites>FETCH-LOGICAL-c288t-bc9a1b6eafeab96ecdd0f1950f1651087ee20e9aeffafdb2be887dc838601e513</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Kiselev, E. A.</creatorcontrib><creatorcontrib>Minin, L. A.</creatorcontrib><creatorcontrib>Novikov, I. Ya</creatorcontrib><creatorcontrib>Sitnik, S. M.</creatorcontrib><title>On the Riesz constants for systems of integer translates</title><title>Mathematical Notes</title><addtitle>Math Notes</addtitle><description>In this paper, one-parameter families of integer translates of the Gaussian and Lorentz functions are studied. For a Lorentz function, we obtain formulas for the coefficients of the series defining node functions and show that the limit value of node functions is given by a sample function. For systems of translates generated by the Gaussian and Lorentz functions as well as by the node functions related to them, we obtain explicit expressions for the Riesz constants and study the parameter-dependent behavior of these constants. While proving some of the results of this paper, we establish the monotonicity of a special ratio of two Jacobi theta functions, a fact which is of interest in itself.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0001-4346</issn><issn>1573-8876</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9j91KxDAQhYMoWFcfwLu8QHWmTdP0UhZ_FhYW_LkuaTvRLrupZOLF-vSmrHeCNzMM55zhO0JcI9wglur2BQBQlUqjghoKpU5EhlVd5sbU-lRks5zP-rm4YN6mCzVCJszGy_hB8nkk_pb95DlaH1m6KUg-cKQ9y8nJ0Ud6pyBjsJ53NhJfijNnd0xXv3sh3h7uX5dP-XrzuFrerfO-MCbmXd9Y7DRZR7ZrNPXDAA6bKg1dIZiaqABqLDln3dAVHSXgoTel0YBUYbkQePzbh4k5kGs_w7i34dAitHP19k_1lCmOGU5en7jb7fQVfML8J_QDp-Zb3g</recordid><startdate>20140701</startdate><enddate>20140701</enddate><creator>Kiselev, E. A.</creator><creator>Minin, L. A.</creator><creator>Novikov, I. Ya</creator><creator>Sitnik, S. M.</creator><general>Pleiades Publishing</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20140701</creationdate><title>On the Riesz constants for systems of integer translates</title><author>Kiselev, E. A. ; Minin, L. A. ; Novikov, I. Ya ; Sitnik, S. M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c288t-bc9a1b6eafeab96ecdd0f1950f1651087ee20e9aeffafdb2be887dc838601e513</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kiselev, E. A.</creatorcontrib><creatorcontrib>Minin, L. A.</creatorcontrib><creatorcontrib>Novikov, I. Ya</creatorcontrib><creatorcontrib>Sitnik, S. M.</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematical Notes</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kiselev, E. A.</au><au>Minin, L. A.</au><au>Novikov, I. Ya</au><au>Sitnik, S. M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Riesz constants for systems of integer translates</atitle><jtitle>Mathematical Notes</jtitle><stitle>Math Notes</stitle><date>2014-07-01</date><risdate>2014</risdate><volume>96</volume><issue>1-2</issue><spage>228</spage><epage>238</epage><pages>228-238</pages><issn>0001-4346</issn><eissn>1573-8876</eissn><abstract>In this paper, one-parameter families of integer translates of the Gaussian and Lorentz functions are studied. For a Lorentz function, we obtain formulas for the coefficients of the series defining node functions and show that the limit value of node functions is given by a sample function. For systems of translates generated by the Gaussian and Lorentz functions as well as by the node functions related to them, we obtain explicit expressions for the Riesz constants and study the parameter-dependent behavior of these constants. While proving some of the results of this paper, we establish the monotonicity of a special ratio of two Jacobi theta functions, a fact which is of interest in itself.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0001434614070244</doi><tpages>11</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0001-4346
ispartof Mathematical Notes, 2014-07, Vol.96 (1-2), p.228-238
issn 0001-4346
1573-8876
language eng
recordid cdi_crossref_primary_10_1134_S0001434614070244
source Springer Nature
subjects Mathematics
Mathematics and Statistics
title On the Riesz constants for systems of integer translates
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T10%3A17%3A42IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref_sprin&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20Riesz%20constants%20for%20systems%20of%20integer%20translates&rft.jtitle=Mathematical%20Notes&rft.au=Kiselev,%20E.%20A.&rft.date=2014-07-01&rft.volume=96&rft.issue=1-2&rft.spage=228&rft.epage=238&rft.pages=228-238&rft.issn=0001-4346&rft.eissn=1573-8876&rft_id=info:doi/10.1134/S0001434614070244&rft_dat=%3Ccrossref_sprin%3E10_1134_S0001434614070244%3C/crossref_sprin%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c288t-bc9a1b6eafeab96ecdd0f1950f1651087ee20e9aeffafdb2be887dc838601e513%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true