Proceedings of the American Mathematical Society, Series B最新文献

{"title":"Stability phenomena for resonance arrangements","authors":"Eric Ramos, N. Proudfoot","doi":"10.1090/bproc/71","DOIUrl":"https://doi.org/10.1090/bproc/71","url":null,"abstract":"We prove that the ith graded pieces of the Orlik-Solomon algebras or Artinian Orlik-Terao algebras of resonance arrangements form a finitely generated FS^op-module, thus obtaining information about the growth of their dimensions and restrictions on the irreducible representations of symmetric groups that they contain.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123963055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Loeb extension and Loeb equivalence","authors":"R. Anderson, Haosui Duanmu, David Schrittesser, W. Weiss","doi":"10.1090/bproc/78","DOIUrl":"https://doi.org/10.1090/bproc/78","url":null,"abstract":"In [J. London Math. Soc. 69 (2004), pp. 258–272] Keisler and Sun leave open several questions regarding Loeb equivalence between internal probability spaces; specifically, whether under certain conditions, the Loeb measure construction applied to two such spaces gives rise to the same measure. We present answers to two of these questions, by giving two examples of probability spaces. Moreover, we reduce their third question to the following: Is the internal algebra generated by the union of two Loeb equivalent internal algebras a subset of their common Loeb extension? We also present a sufficient condition for a positive answer to this question.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115330839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The two-sided Pompeiu problem for discrete groups","authors":"P. Linnell, M. Puls","doi":"10.1090/bproc/124","DOIUrl":"https://doi.org/10.1090/bproc/124","url":null,"abstract":"<p>We consider a two-sided Pompeiu type problem for a discrete group <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>. We give necessary and sufficient conditions for a finite subset <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\">\u0000 <mml:semantics>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">K</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> 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> to have the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper F left-parenthesis upper G right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">F</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {F}(G)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-Pompeiu property. Using group von Neumann algebra techniques, we give necessary and sufficient conditions for <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> to be an <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script l squared left-parenthesis upper G right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msup>\u0000 <mml:mi>ℓ<!-- ℓ --></mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msup>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">ell ^2(G)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-Pompeiu group.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127641156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Differential Brauer monoids","authors":"A. Magid","doi":"10.1090/bproc/162","DOIUrl":"https://doi.org/10.1090/bproc/162","url":null,"abstract":"The differential Brauer monoid of a differential commutative ring \u0000\u0000 \u0000 R\u0000 R\u0000 \u0000\u0000 is defined. Its elements are the isomorphism classes of differential Azumaya \u0000\u0000 \u0000 R\u0000 R\u0000 \u0000\u0000 algebras with operation from tensor product subject to the relation that two such algebras are equivalent if matrix algebras over them, with entry-wise differentiation, are differentially isomorphic. The fine Bauer monoid, which is a group, is the same thing without the differential requirement. The differential Brauer monoid is then determined from the fine Brauer monoids of \u0000\u0000 \u0000 R\u0000 R\u0000 \u0000\u0000 and \u0000\u0000 \u0000 \u0000 R\u0000 D\u0000 \u0000 R^D\u0000 \u0000\u0000 and the submonoid of the Brauer monoid whose underlying Azumaya algebras are matrix rings.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114506818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interpolation in model spaces","authors":"P. Gorkin, B. Wick","doi":"10.1090/bproc/59","DOIUrl":"https://doi.org/10.1090/bproc/59","url":null,"abstract":"In this paper we consider interpolation in model spaces, $H^2 ominus B H^2$ with $B$ a Blaschke product. We study unions of interpolating sequences for two sequences that are far from each other in the pseudohyperbolic metric as well as two sequences that are close to each other in the pseudohyperbolic metric. The paper concludes with a discussion of the behavior of Frostman sequences under perturbations.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122723323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The product formula for regularized Fredholm determinants","authors":"Thomas Britz, A. Carey, F. Gesztesy, Roger Nichols, F. Sukochev, D. Zanin","doi":"10.1090/BPROC/70","DOIUrl":"https://doi.org/10.1090/BPROC/70","url":null,"abstract":"For trace class operators $A, B in mathcal{B}_1(mathcal{H})$ ($mathcal{H}$ a complex, separable Hilbert space), the product formula for Fredholm determinants holds in the familiar form [ {det}_{mathcal{H}} ((I_{mathcal{H}} - A) (I_{mathcal{H}} - B)) = {det}_{mathcal{H}} (I_{mathcal{H}} - A) {det}_{mathcal{H}} (I_{mathcal{H}} - B). ] When trace class operators are replaced by Hilbert--Schmidt operators $A, B in mathcal{B}_2(mathcal{H})$ and the Fredholm determinant ${det}_{mathcal{H}}(I_{mathcal{H}} - A)$, $A in mathcal{B}_1(mathcal{H})$, by the 2nd regularized Fredholm determinant ${det}_{mathcal{H},2}(I_{mathcal{H}} - A) = {det}_{mathcal{H}} ((I_{mathcal{H}} - A) exp(A))$, $A in mathcal{B}_2(mathcal{H})$, the product formula must be replaced by [ {det}_{mathcal{H},2} ((I_{mathcal{H}} - A) (I_{mathcal{H}} - B)) = {det}_{mathcal{H},2} (I_{mathcal{H}} - A) {det}_{mathcal{H},2} (I_{mathcal{H}} - B) exp(- {rm tr}(AB)). ] The product formula for the case of higher regularized Fredholm determinants ${det}_{mathcal{H},k}(I_{mathcal{H}} - A)$, $A in mathcal{B}_k(mathcal{H})$, $k in mathbb{N}$, $k geq 2$, does not seem to be easily accessible and hence this note aims at filling this gap in the literature.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116765260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Abelian maps, bi-skew braces, and opposite pairs of Hopf-Galois structures","authors":"Alan Koch","doi":"10.1090/BPROC/87","DOIUrl":"https://doi.org/10.1090/BPROC/87","url":null,"abstract":"Let \u0000\u0000 \u0000 G\u0000 G\u0000 \u0000\u0000 be a finite nonabelian group, and let \u0000\u0000 \u0000 \u0000 ψ\u0000 :\u0000 G\u0000 →\u0000 G\u0000 \u0000 psi :Gto G\u0000 \u0000\u0000 be a homomorphism with abelian image. We show how \u0000\u0000 \u0000 ψ\u0000 psi\u0000 \u0000\u0000 gives rise to two Hopf-Galois structures on a Galois extension \u0000\u0000 \u0000 \u0000 L\u0000 \u0000 /\u0000 \u0000 K\u0000 \u0000 L/K\u0000 \u0000\u0000 with Galois group (isomorphic to) \u0000\u0000 \u0000 G\u0000 G\u0000 \u0000\u0000; one of these structures generalizes the construction given by a “fixed point free abelian endomorphism” introduced by Childs in 2013. We construct the skew left brace corresponding to each of the two Hopf-Galois structures above. We will show that one of the skew left braces is in fact a bi-skew brace, allowing us to obtain four set-theoretic solutions to the Yang-Baxter equation as well as a pair of Hopf-Galois structures on a (potentially) different finite Galois extension.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134547286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bounded complexes of permutation modules","authors":"D. Benson, J. Carlson","doi":"10.1090/bproc/102","DOIUrl":"https://doi.org/10.1090/bproc/102","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\">\u0000 <mml:semantics>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">k</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be a field of characteristic <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p greater-than 0\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mo>></mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">p > 0</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. For <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> an elementary abelian <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>-group, there exist collections of permutation modules such that if <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript asterisk\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>C</mml:mi>\u0000 <mml:mo>∗<!-- ∗ --></mml:mo>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">C^*</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is any exact bounded complex whose terms are sums of copies of modules from the collection, then <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript asterisk\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>C</mml:mi>\u0000 <mml:mo>∗<!-- ∗ --></mml:mo>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">C^*</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is contractible. A consequence is that if <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> is any finite group whose Sylow <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>-subgroups are not cyclic or quaternion, and if <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript asterisk\">\u0000 <mml:semantics>\u0000 <mml:","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123748095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Amplified graph C*-algebras II: Reconstruction","authors":"S. Eilers, Efren Ruiz, A. Sims","doi":"10.1090/bproc/112","DOIUrl":"https://doi.org/10.1090/bproc/112","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 E\">\u0000 <mml:semantics>\u0000 <mml:mi>E</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">E</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be a countable directed graph that is amplified in the sense that whenever there is an edge from <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"v\">\u0000 <mml:semantics>\u0000 <mml:mi>v</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">v</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> to <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"w\">\u0000 <mml:semantics>\u0000 <mml:mi>w</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">w</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, there are infinitely many edges from <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"v\">\u0000 <mml:semantics>\u0000 <mml:mi>v</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">v</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> to <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"w\">\u0000 <mml:semantics>\u0000 <mml:mi>w</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">w</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. We show that <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E\">\u0000 <mml:semantics>\u0000 <mml:mi>E</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">E</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> can be recovered from <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript asterisk Baseline left-parenthesis upper E right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msup>\u0000 <mml:mi>C</mml:mi>\u0000 <mml:mo>∗<!-- ∗ --></mml:mo>\u0000 </mml:msup>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>E</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">C^*(E)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> together with its canonical gauge-action, and also from <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Subscript double-struck upper K Baseline left-parenthesis upper E right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">K</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>E</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132616950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a quaternionic Picard theorem","authors":"C. Bisi, J. Winkelmann","doi":"10.1090/bproc/54","DOIUrl":"https://doi.org/10.1090/bproc/54","url":null,"abstract":"<p>The classical theorem of Picard states that a non-constant holomorphic function <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f colon double-struck upper C right-arrow double-struck upper C\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mo>:</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">C</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo stretchy=\"false\">→<!-- → --></mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">C</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">f:mathbb {C}to mathbb {C}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> can avoid at most one value.</p>\u0000\u0000<p>We investigate how many values a non-constant slice regular function of a quaternionic variable <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f colon double-struck upper H right-arrow double-struck upper H\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mo>:</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">H</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo stretchy=\"false\">→<!-- → --></mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">H</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">f:mathbb {H}to mathbb {H}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> may avoid.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114673829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}