In 2020, Chalmoukis introduced a generalization of the Volterra operator and studied its boundedness and compactness on Hardy spaces. Inspired by Chalmoukis (2020), Li, Liu and Lou (2014), and Li, Liu and Yuan (2020), we study the boundedness and compactness of the generalized Volterra operator on analytic Morrey spaces and Dirichlet type spaces.
在2020年，Chalmoukis引入了Volterra算子的推广，并研究了它在Hardy空间上的有界性和紧性。受Chalmoukis(2020)、Li, Liu and Lou(2014)和Li, Liu and Yuan(2020)的启发，我们研究了解析Morrey空间和Dirichlet型空间上广义Volterra算子的有界性和紧性。
{"title":"GENERALIZED INTEGRATION OPERATORS ON SOME BANACH SPACES OF ANALYTIC FUNCTIONS","authors":"Mingshan Li, Zhenyou Wang","doi":"10.1216/jie.2023.35.339","DOIUrl":"https://doi.org/10.1216/jie.2023.35.339","url":null,"abstract":"In 2020, Chalmoukis introduced a generalization of the Volterra operator and studied its boundedness and compactness on Hardy spaces. Inspired by Chalmoukis (2020), Li, Liu and Lou (2014), and Li, Liu and Yuan (2020), we study the boundedness and compactness of the generalized Volterra operator on analytic Morrey spaces and Dirichlet type spaces.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136093569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A NOVEL METHOD FOR LINEAR AND NONLINEAR FRACTIONAL VOLTERRA INTEGRAL EQUATIONS VIA CUBIC HAT FUNCTIONS","authors":"Hamed Ebrahimi, Jafar Biazar","doi":"10.1216/jie.2023.35.291","DOIUrl":"https://doi.org/10.1216/jie.2023.35.291","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136167274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"EXISTENCE, UNIQUENESS AND ABSTRACT APPROACH TO HYERS–ULAM STABILITY IN BANACH LATTICE ALGEBRAS AND AN APPLICATION","authors":"Nadir Benkaci-Ali","doi":"10.1216/jie.2023.35.259","DOIUrl":"https://doi.org/10.1216/jie.2023.35.259","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136168127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
By a probabilistic approach, we look at an obstacle problem with nonlinear Neumann boundary conditions for parabolic semilinear integral-partial differential equations. We prove the existence of a continuous viscosity solution of this problem. The nonlinear part of the equation and the Neumann condition satisfy the stochastic monotonicity condition on the solution variable. Furthermore, the nonlinear part is stochastic Lipschitz on the parts that depend on the gradient and the integral of the solution. It should be noted that the existence of the viscosity solution for this problem has recently been investigated using a standard monotonicity and Lipschitz conditions. We show that the solution of the related reflected generalized backward stochastic differential equations with jumps exists and is unique when the barrier is right continuous left limited (rcll) and the generators satisfy stochastic monotonicity and Lipschitz conditions. In this case, we get a comparison result.
{"title":"REFLECTED GENERALIZED BSDE WITH JUMPS UNDER STOCHASTIC CONDITIONS AND AN OBSTACLE PROBLEM FOR INTEGRAL-PARTIAL DIFFERENTIAL EQUATIONS WITH NONLINEAR NEUMANN BOUNDARY CONDITIONS","authors":"Mohammed Elhachemy, Mohamed El Otmani","doi":"10.1216/jie.2023.35.311","DOIUrl":"https://doi.org/10.1216/jie.2023.35.311","url":null,"abstract":"By a probabilistic approach, we look at an obstacle problem with nonlinear Neumann boundary conditions for parabolic semilinear integral-partial differential equations. We prove the existence of a continuous viscosity solution of this problem. The nonlinear part of the equation and the Neumann condition satisfy the stochastic monotonicity condition on the solution variable. Furthermore, the nonlinear part is stochastic Lipschitz on the parts that depend on the gradient and the integral of the solution. It should be noted that the existence of the viscosity solution for this problem has recently been investigated using a standard monotonicity and Lipschitz conditions. We show that the solution of the related reflected generalized backward stochastic differential equations with jumps exists and is unique when the barrier is right continuous left limited (rcll) and the generators satisfy stochastic monotonicity and Lipschitz conditions. In this case, we get a comparison result.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136093448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"MONOTONICITY OF STANDING WAVES FOR THE GENERALIZED FRACTIONAL SCHRÖDINGER EQUATIONS","authors":"Yajie Zhang, Feiyao Ma, Weifeng Wo","doi":"10.1216/jie.2023.35.375","DOIUrl":"https://doi.org/10.1216/jie.2023.35.375","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136167815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"SOLVABILITY FOR FRACTIONAL INTEGRAL EQUATIONS VIA PETRYSHYN’S FIXED-POINT THEOREM","authors":"Amar Deep, Deepika Saini, Hitesh Kumar Singh, Ümit Çakan","doi":"10.1216/jie.2023.35.277","DOIUrl":"https://doi.org/10.1216/jie.2023.35.277","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136167824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Electrocardiogram (EMG) signals play a significant role in decoding muscle contraction information for robotic hand prosthesis controllers. Widely applied decoders require large amount of EMG signals sensors, resulting in complicated calculations and unsatisfactory predictions. By the biomechanical process of single degree-of-freedom human hand movements, only several EMG signals are essential for accurate predictions. Recently, a novel predictor of hand movements adopts a multistage Sequential, Adaptive Functional Estimation (SAFE) method based on historical Functional Linear Model (FLM) to select important EMG signals and provide precise projections. However, SAFE repeatedly performs matrix-vector multiplications with a dense representation matrix of the integral operator for the FLM, which is computational expansive. Noting that with a properly chosen basis, the representation of the integral operator concentrates on a few bands of the basis, the goal of this study is to develop a fast Multiscale SAFE (MSAFE) method aiming at reducing computational costs while preserving (or even improving) the accuracy of the original SAFE method. Specifically, a multiscale piecewise polynomial basis is adopted to discretize the integral operator for the FLM, resulting in an approximately sparse representation matrix, and then the matrix is truncated to a sparse one. This approach not only accelerates computations but also improves robustness against noises. When applied to real hand movement data, MSAFE saves 85%$sim$90% computing time compared with SAFE, while producing better sensor selection and comparable accuracy. In a simulation study, MSAFE shows stronger stability in sensor selection and prediction accuracy against correlated noise than SAFE.
{"title":"FAST MULTISCALE FUNCTIONAL ESTIMATION IN OPTIMAL EMG PLACEMENT FOR ROBOTIC PROSTHESIS CONTROLLERS","authors":"Jin Ren, Guohui Song, Lucia Tabacu, Yuesheng Xu","doi":"10.1216/jie.2023.35.355","DOIUrl":"https://doi.org/10.1216/jie.2023.35.355","url":null,"abstract":"Electrocardiogram (EMG) signals play a significant role in decoding muscle contraction information for robotic hand prosthesis controllers. Widely applied decoders require large amount of EMG signals sensors, resulting in complicated calculations and unsatisfactory predictions. By the biomechanical process of single degree-of-freedom human hand movements, only several EMG signals are essential for accurate predictions. Recently, a novel predictor of hand movements adopts a multistage Sequential, Adaptive Functional Estimation (SAFE) method based on historical Functional Linear Model (FLM) to select important EMG signals and provide precise projections. However, SAFE repeatedly performs matrix-vector multiplications with a dense representation matrix of the integral operator for the FLM, which is computational expansive. Noting that with a properly chosen basis, the representation of the integral operator concentrates on a few bands of the basis, the goal of this study is to develop a fast Multiscale SAFE (MSAFE) method aiming at reducing computational costs while preserving (or even improving) the accuracy of the original SAFE method. Specifically, a multiscale piecewise polynomial basis is adopted to discretize the integral operator for the FLM, resulting in an approximately sparse representation matrix, and then the matrix is truncated to a sparse one. This approach not only accelerates computations but also improves robustness against noises. When applied to real hand movement data, MSAFE saves 85%$sim$90% computing time compared with SAFE, while producing better sensor selection and comparable accuracy. In a simulation study, MSAFE shows stronger stability in sensor selection and prediction accuracy against correlated noise than SAFE.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136167059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"COMPACT INTERTWINING RELATIONS FOR COMPOSITION OPERATORS BETWEEN MORREY SPACES AND BLOCH-TYPE SPACES","authors":"Mao Xiao, Junming Liu","doi":"10.1216/jie.2023.35.215","DOIUrl":"https://doi.org/10.1216/jie.2023.35.215","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135195499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"VOLTERRA INTEGRAL OPERATORS FROM MORREY-TYPE SPACES TO DIRICHLET–MORREY TYPE SPACES","authors":"Ruishen Qian","doi":"10.1216/jie.2023.35.131","DOIUrl":"https://doi.org/10.1216/jie.2023.35.131","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135195503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"VOLTERRA AND FREDHOLM INTEGRAL EQUATIONS IN LOCALLY CONVEX SPACES, AND LEADER-TYPE CONTRACTIONS IN GAUGE SPACES","authors":"Kazimierz Włodarczyk","doi":"10.1216/jie.2023.35.141","DOIUrl":"https://doi.org/10.1216/jie.2023.35.141","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135195505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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