Pub Date : 2023-11-14DOI: 10.1007/s00020-023-02751-6
Michael T. Jury, Georgios Tsikalas
{"title":"Denjoy–Wolff Points on the Bidisk via Models","authors":"Michael T. Jury, Georgios Tsikalas","doi":"10.1007/s00020-023-02751-6","DOIUrl":"https://doi.org/10.1007/s00020-023-02751-6","url":null,"abstract":"","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134902650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-12DOI: 10.1007/s00020-023-02750-7
Martin Costabel, Monique Dauge, Khadijeh Nedaiasl
{"title":"Stability Analysis of a Simple Discretization Method for a Class of Strongly Singular Integral Equations","authors":"Martin Costabel, Monique Dauge, Khadijeh Nedaiasl","doi":"10.1007/s00020-023-02750-7","DOIUrl":"https://doi.org/10.1007/s00020-023-02750-7","url":null,"abstract":"","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135037590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-12DOI: 10.1007/s00020-023-02748-1
Masashi Wakaiki
Abstract This paper is concerned with the decay rate of $$e^{A^{-1}t}A^{-1}$$ eA-1tA-1 for the generator A of an exponentially stable $$C_0$$ C0 -semigroup on a Hilbert space. To estimate the decay rate of $$e^{A^{-1}t}A^{-1}$$ eA-1tA-1 , we apply a bounded functional calculus. Using this estimate and Lyapunov equations, we also study the quantified asymptotic behavior of the Crank-Nicolson scheme with smooth initial data. A similar argument is applied to a polynomially stable $$C_0$$ C0 -semigroup whose generator is normal.
研究Hilbert空间上指数稳定的$$C_0$$ c0 -半群的生成子A的衰减率($$e^{A^{-1}t}A^{-1}$$ e A - 1)和(A - 1)。为了估计$$e^{A^{-1}t}A^{-1}$$ e A - 1 t A - 1的衰减率，我们应用了有界泛函演算。利用这个估计和Lyapunov方程，我们还研究了具有光滑初始数据的Crank-Nicolson格式的量化渐近行为。一个类似的论证被应用于多项式稳定的$$C_0$$ C 0 -半群，它的生成器是正常的。
{"title":"Decay Rate of $$varvec{exp (A^{-1}t)A^{-1}}$$ on a Hilbert Space and the Crank–Nicolson Scheme with Smooth Initial Data","authors":"Masashi Wakaiki","doi":"10.1007/s00020-023-02748-1","DOIUrl":"https://doi.org/10.1007/s00020-023-02748-1","url":null,"abstract":"Abstract This paper is concerned with the decay rate of $$e^{A^{-1}t}A^{-1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:msup> <mml:mi>A</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mi>t</mml:mi> </mml:mrow> </mml:msup> <mml:msup> <mml:mi>A</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> for the generator A of an exponentially stable $$C_0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> -semigroup on a Hilbert space. To estimate the decay rate of $$e^{A^{-1}t}A^{-1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:msup> <mml:mi>A</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mi>t</mml:mi> </mml:mrow> </mml:msup> <mml:msup> <mml:mi>A</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , we apply a bounded functional calculus. Using this estimate and Lyapunov equations, we also study the quantified asymptotic behavior of the Crank-Nicolson scheme with smooth initial data. A similar argument is applied to a polynomially stable $$C_0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> -semigroup whose generator is normal.","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135037286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-07DOI: 10.1007/s00020-023-02749-0
Sam Farrington, Katie Gittins
Abstract We investigate the heat flow in an open, bounded set D in $$mathbb {R}^2$$ R2 with polygonal boundary $$partial D$$ ∂D . We suppose that D contains an open, bounded set $$widetilde{D}$$ D~ with polygonal boundary $$partial widetilde{D}$$ ∂D~ . The initial condition is the indicator function of $$widetilde{D}$$ D~ and we impose a Neumann boundary condition on the edges of $$partial D$$ ∂D . We obtain an asymptotic formula for the heat content of $$widetilde{D}$$ D~ in D as time $$tdownarrow 0$$ t↓0 .
{"title":"Heat Flow in Polygons with Reflecting Edges","authors":"Sam Farrington, Katie Gittins","doi":"10.1007/s00020-023-02749-0","DOIUrl":"https://doi.org/10.1007/s00020-023-02749-0","url":null,"abstract":"Abstract We investigate the heat flow in an open, bounded set D in $$mathbb {R}^2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:math> with polygonal boundary $$partial D$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>∂</mml:mi> <mml:mi>D</mml:mi> </mml:mrow> </mml:math> . We suppose that D contains an open, bounded set $$widetilde{D}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> with polygonal boundary $$partial widetilde{D}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>∂</mml:mi> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:mrow> </mml:math> . The initial condition is the indicator function of $$widetilde{D}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> and we impose a Neumann boundary condition on the edges of $$partial D$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>∂</mml:mi> <mml:mi>D</mml:mi> </mml:mrow> </mml:math> . We obtain an asymptotic formula for the heat content of $$widetilde{D}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> in D as time $$tdownarrow 0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>↓</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> .","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135474920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-07DOI: 10.1007/s00020-023-02747-2
Weisz Ferenc, Guangheng Xie, Dachun Yang
{"title":"Dyadic Maximal Operators on Martingale Musielak–Orlicz Hardy Type Spaces and Applications","authors":"Weisz Ferenc, Guangheng Xie, Dachun Yang","doi":"10.1007/s00020-023-02747-2","DOIUrl":"https://doi.org/10.1007/s00020-023-02747-2","url":null,"abstract":"","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135476598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-12DOI: 10.1007/s00020-023-02745-4
Youqing Ji, Yuanhang Zhang
{"title":"On the Power Set of Quasinilpotent Operators","authors":"Youqing Ji, Yuanhang Zhang","doi":"10.1007/s00020-023-02745-4","DOIUrl":"https://doi.org/10.1007/s00020-023-02745-4","url":null,"abstract":"","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135970084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-22DOI: 10.1007/s00020-023-02744-5
Lars Perlich
{"title":"Semiflows, Composition Semigroups, and the Approximation of Dirichlet-to-Neumann Semigroups","authors":"Lars Perlich","doi":"10.1007/s00020-023-02744-5","DOIUrl":"https://doi.org/10.1007/s00020-023-02744-5","url":null,"abstract":"","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136060442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-25DOI: 10.1007/s00020-023-02738-3
C. Guiver, M. Opmeer
{"title":"Representations and Regularity of Vector-Valued Right-Shift Invariant Operators Between Half-Line Bessel Potential Spaces","authors":"C. Guiver, M. Opmeer","doi":"10.1007/s00020-023-02738-3","DOIUrl":"https://doi.org/10.1007/s00020-023-02738-3","url":null,"abstract":"","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44074256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：