Memoirs of the American Mathematical Society最新文献

{"title":"Ergodicity of Markov Processes via Nonstandard Analysis","authors":"Haosui Duanmu, J. Rosenthal, W. Weiss","doi":"10.1090/memo/1342","DOIUrl":"https://doi.org/10.1090/memo/1342","url":null,"abstract":"The Markov chain ergodic theorem is well-understood if either the time-line or the state space is discrete. However, there does not exist a very clear result for general state space continuous-time Markov processes. Using methods from mathematical logic and nonstandard analysis, we introduce a class of hyperfinite Markov processes-namely, general Markov processes which behave like finite state space discrete-time Markov processes. We show that, under moderate conditions, the transition probability of hyperfinite Markov processes align with the transition probability of standard Markov processes. The Markov chain ergodic theorem for hyperfinite Markov processes will then imply the Markov chain ergodic theorem for general state space continuous-time Markov processes.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43809879","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":"Corrigendum and improvements to “Carleman estimates, observability inequalities and null controllability for interior degenerate non smooth parabolic equations”, and its consequences","authors":"G. Fragnelli, Dimitri Mugnai","doi":"10.1090/memo/1332","DOIUrl":"https://doi.org/10.1090/memo/1332","url":null,"abstract":"This paper is a corrigendum of one hypothesis introduced in Mem. Amer. Math. Soc. 242 (2016), no. 1146, and used again in J. Differential Equations 260 (2016), pp. 1314–1371 and Adv. Nonlinear Anal. 6 (2017), pp. 61–84]. We give here the corrected proofs of the concerned results, improving most of them.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42212631","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":"Model theory of 𝐶*-algebras","authors":"I. Farah, B. Hart, M. Lupini, L. Robert, A. Tikuisis, A. Vignati, W. Winter","doi":"10.1090/memo/1324","DOIUrl":"https://doi.org/10.1090/memo/1324","url":null,"abstract":"","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":"19 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60558747","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":"Galois and cleft monoidal cowreaths. Applications","authors":"D. Bulacu, B. Torrecillas","doi":"10.1090/memo/1322","DOIUrl":"https://doi.org/10.1090/memo/1322","url":null,"abstract":"","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44166451","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":"On Medium-Rank Lie Primitive and Maximal Subgroups of Exceptional Groups of Lie Type","authors":"David A. Craven","doi":"10.1090/memo/1434","DOIUrl":"https://doi.org/10.1090/memo/1434","url":null,"abstract":"<p>We study embeddings of groups of Lie type <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H\">\u0000 <mml:semantics>\u0000 <mml:mi>H</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">H</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> in characteristic <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\u0000 <mml:semantics>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">p</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> into exceptional algebraic groups <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"bold upper G\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"bold\">G</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbf {G}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of the same characteristic. We exclude the case where <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H\">\u0000 <mml:semantics>\u0000 <mml:mi>H</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">H</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is of type <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper P normal upper S normal upper L Subscript 2\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">P</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">S</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">L</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathrm {PSL}_2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. A subgroup of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"bold upper G\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"bold\">G</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbf {G}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is <italic>Lie primitive</italic> if it is not contained in any proper, positive-dimensional subgroup of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"bold upper G\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"bold\">G</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbf {G}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>.</p>\u0000\u0000<p>With a few possible exceptions, we prove that there are no Lie primitive subgroups <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H\"","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41510240","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":"The 2D compressible Euler equations in\u0000 bounded impermeable domains with corners","authors":"P. Godin","doi":"10.1090/MEMO/1313","DOIUrl":"https://doi.org/10.1090/MEMO/1313","url":null,"abstract":"","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":"269 1","pages":"0-0"},"PeriodicalIF":1.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60559126","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":"Hecke Operators and Systems of Eigenvalues on\u0000 Siegel Cusp Forms","authors":"Kazuyuki Hatada","doi":"10.1090/memo/1306","DOIUrl":"https://doi.org/10.1090/memo/1306","url":null,"abstract":"","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":"19 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86973114","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":"On stability of type II blow up for the\u0000 critical nonlinear wave equation on ℝ³⁺¹","authors":"J. Krieger","doi":"10.1090/memo/1301","DOIUrl":"https://doi.org/10.1090/memo/1301","url":null,"abstract":"","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":"267 1","pages":"0-0"},"PeriodicalIF":1.9,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47815017","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":"Deformation and Unobstructedness of Determinantal Schemes","authors":"Jan O. Kleppe, R. Mir'o-Roig","doi":"10.1090/memo/1418","DOIUrl":"https://doi.org/10.1090/memo/1418","url":null,"abstract":"<p>A closed subscheme <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X subset-of double-struck upper P Superscript n\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo>⊂<!-- ⊂ --></mml:mo>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">P</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Xsubset mathbb {P}^n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is said to be <italic>determinantal</italic> if its homogeneous saturated ideal can be generated by the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"s times s\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:mo>×<!-- × --></mml:mo>\u0000 <mml:mi>s</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">stimes s</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> minors of a homogeneous <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p times q\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mo>×<!-- × --></mml:mo>\u0000 <mml:mi>q</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">ptimes q</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> matrix satisfying <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis p minus s plus 1 right-parenthesis left-parenthesis q minus s plus 1 right-parenthesis equals n minus dimension upper X\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>q</mml:mi>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mi>dim</mml:mi>\u0000 <mml:mo>⁡<!-- ⁡ --></mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(p-s+1)(q-s+1)=n - dim X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and it is said to be <italic>standard determinantal</italic> if, in addition, <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"s equals min left-parenthesis p comma q right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mo movablelimits=\"true\" form=\"prefix\">min</mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43494237","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":"Unitarizability in Corank Three for Classical 𝑝-adic Groups","authors":"Marko Tadić","doi":"10.1090/memo/1421","DOIUrl":"https://doi.org/10.1090/memo/1421","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\">\u0000 <mml:semantics>\u0000 <mml:mi>F</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">F</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-points of a classical group defined over a <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\u0000 <mml:semantics>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">p</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-adic field <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\">\u0000 <mml:semantics>\u0000 <mml:mi>F</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">F</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of characteristic <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"0\">\u0000 <mml:semantics>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">0</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. We classify the irreducible unitarizable representation of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> that are subquotients of the parabolic induction of cuspidal representations of Levi subgroup of corank at most 3 in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>.</p>","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46100343","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}