Pub Date : 2022-06-11DOI: 10.1007/s00032-022-00356-z
F. Anella, D. Huybrechts
{"title":"Effectivity of Semi-positive Line Bundles","authors":"F. Anella, D. Huybrechts","doi":"10.1007/s00032-022-00356-z","DOIUrl":"https://doi.org/10.1007/s00032-022-00356-z","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42701042","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 : 2022-06-05DOI: 10.1007/s00032-023-00378-1
A. Baranov
{"title":"Cauchy–de Branges Spaces, Geometry of Their Reproducing Kernels and Multiplication Operators","authors":"A. Baranov","doi":"10.1007/s00032-023-00378-1","DOIUrl":"https://doi.org/10.1007/s00032-023-00378-1","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44055025","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 : 2022-06-03DOI: 10.1007/s00032-022-00355-0
Julián Agredo, Franco Fagnola, Damiano Poletti
We demonstrate a method for finding the decoherence-free subalgebra ({mathcal {N}}({mathcal {T}})) of a Gaussian quantum Markov semigroup on the von Neumann algebra ({mathcal {B}}(Gamma (mathbb {C}^d))) of all bounded operator on the Fock space (Gamma (mathbb {C}^d)) on (mathbb {C}^d). We show that ({mathcal {N}}({mathcal {T}})) is a type I von Neumann algebra (L^infty (mathbb {R}^{d_c};mathbb {C}){overline{otimes }}{mathcal {B}}(Gamma (mathbb {C}^{d_f}))) determined, up to unitary equivalence, by two natural numbers (d_c,d_fle d). This result is illustrated by some applications and examples.
{"title":"The Decoherence-Free Subalgebra of Gaussian Quantum Markov Semigroups","authors":"Julián Agredo, Franco Fagnola, Damiano Poletti","doi":"10.1007/s00032-022-00355-0","DOIUrl":"https://doi.org/10.1007/s00032-022-00355-0","url":null,"abstract":"<p>We demonstrate a method for finding the decoherence-free subalgebra <span>({mathcal {N}}({mathcal {T}}))</span> of a Gaussian quantum Markov semigroup on the von Neumann algebra <span>({mathcal {B}}(Gamma (mathbb {C}^d)))</span> of all bounded operator on the Fock space <span>(Gamma (mathbb {C}^d))</span> on <span>(mathbb {C}^d)</span>. We show that <span>({mathcal {N}}({mathcal {T}}))</span> is a type I von Neumann algebra <span>(L^infty (mathbb {R}^{d_c};mathbb {C}){overline{otimes }}{mathcal {B}}(Gamma (mathbb {C}^{d_f})))</span> determined, up to unitary equivalence, by two natural numbers <span>(d_c,d_fle d)</span>. This result is illustrated by some applications and examples.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495282","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 : 2022-05-25DOI: 10.1007/s00032-022-00373-y
C. Marchionna, S. Panizzi
{"title":"Transfer of Energy from Flexural to Torsional Modes for the Fish-Bone Suspension Bridge Model","authors":"C. Marchionna, S. Panizzi","doi":"10.1007/s00032-022-00373-y","DOIUrl":"https://doi.org/10.1007/s00032-022-00373-y","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41986655","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 : 2022-05-21DOI: 10.1007/s00032-022-00351-4
Simone Cerreia-Vioglio, Paolo Leonetti, Fabio Maccheroni
Given a probability measure space ((X,Sigma ,mu )), it is well known that the Riesz space (L^0(mu )) of equivalence classes of measurable functions (f: X rightarrow mathbf {R}) is universally complete and the constant function (varvec{1}) is a weak order unit. Moreover, the linear functional (L^infty (mu )rightarrow mathbf {R}) defined by (f mapsto int f,mathrm {d}mu ) is strictly positive and order continuous. Here we show, in particular, that the converse holds true, i.e., any universally complete Riesz space E with a weak order unit (e>0) which admits a strictly positive order continuous linear functional on the principal ideal generated by e is lattice isomorphic onto (L^0(mu )), for some probability measure space ((X,Sigma ,mu )).
给定一个概率测度空间((X,Sigma ,mu ))，已知可测函数的等价类(f: X rightarrow mathbf {R})的Riesz空间(L^0(mu ))是普遍完备的，常数函数(varvec{1})是一个弱序单元。并且，由(f mapsto int f,mathrm {d}mu )定义的线性泛函(L^infty (mu )rightarrow mathbf {R})是严格正的、序连续的。这里我们特别证明了相反的命题成立，即对于某些概率测度空间((X,Sigma ,mu ))，任何具有弱阶单位(e>0)的普遍完备Riesz空间E在主理想上允许一个严格正阶连续线性泛函在(L^0(mu ))上是格同构的。
{"title":"A Characterization of the Vector Lattice of Measurable Functions","authors":"Simone Cerreia-Vioglio, Paolo Leonetti, Fabio Maccheroni","doi":"10.1007/s00032-022-00351-4","DOIUrl":"https://doi.org/10.1007/s00032-022-00351-4","url":null,"abstract":"<p>Given a probability measure space <span>((X,Sigma ,mu ))</span>, it is well known that the Riesz space <span>(L^0(mu ))</span> of equivalence classes of measurable functions <span>(f: X rightarrow mathbf {R})</span> is universally complete and the constant function <span>(varvec{1})</span> is a weak order unit. Moreover, the linear functional <span>(L^infty (mu )rightarrow mathbf {R})</span> defined by <span>(f mapsto int f,mathrm {d}mu )</span> is strictly positive and order continuous. Here we show, in particular, that the converse holds true, i.e., any universally complete Riesz space <i>E</i> with a weak order unit <span>(e>0)</span> which admits a strictly positive order continuous linear functional on the principal ideal generated by <i>e</i> is lattice isomorphic onto <span>(L^0(mu ))</span>, for some probability measure space <span>((X,Sigma ,mu ))</span>.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495281","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 : 2022-04-25DOI: 10.1007/s00032-022-00354-1
M. Cuesta, R. Pardo
{"title":"Positive Solutions for Slightly Subcritical Elliptic Problems Via Orlicz Spaces","authors":"M. Cuesta, R. Pardo","doi":"10.1007/s00032-022-00354-1","DOIUrl":"https://doi.org/10.1007/s00032-022-00354-1","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45465386","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 : 2022-04-17DOI: 10.1007/s00032-023-00377-2
R. K. Giri, Y. Pinchover
{"title":"Positive Solutions of Quasilinear Elliptic Equations with Fuchsian Potentials in Wolff Class","authors":"R. K. Giri, Y. Pinchover","doi":"10.1007/s00032-023-00377-2","DOIUrl":"https://doi.org/10.1007/s00032-023-00377-2","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46145140","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 : 2022-03-28DOI: 10.1007/s00032-022-00352-3
Giulia Furioli, Ada Pulvirenti, Elide Terraneo, Giuseppe Toscani
We present and discuss connections between the problem of trend to equilibrium for one-dimensional Fokker–Planck equations modeling socio-economic problems, and one-dimensional functional inequalities of the type of Poincaré, Wirtinger and logarithmic Sobolev, with weight, for probability densities with polynomial tails. As main examples, we consider inequalities satisfied by inverse Gamma densities, taking values on (mathbb R_+), and Cauchy-type densities, taking values on (mathbb R).
{"title":"One-Dimensional Fokker–Planck Equations and Functional Inequalities for Heavy Tailed Densities","authors":"Giulia Furioli, Ada Pulvirenti, Elide Terraneo, Giuseppe Toscani","doi":"10.1007/s00032-022-00352-3","DOIUrl":"https://doi.org/10.1007/s00032-022-00352-3","url":null,"abstract":"<p>We present and discuss connections between the problem of trend to equilibrium for one-dimensional Fokker–Planck equations modeling socio-economic problems, and one-dimensional functional inequalities of the type of Poincaré, Wirtinger and logarithmic Sobolev, with weight, for probability densities with polynomial tails. As main examples, we consider inequalities satisfied by inverse Gamma densities, taking values on <span>(mathbb R_+)</span>, and Cauchy-type densities, taking values on <span>(mathbb R)</span>.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495283","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 : 2022-03-22DOI: 10.1007/s00032-021-00348-5
Ruixin Shen, Mingqi Xiang, V. Rǎdulescu
{"title":"Time-Space Fractional Diffusion Problems: Existence, Decay Estimates and Blow-Up of Solutions","authors":"Ruixin Shen, Mingqi Xiang, V. Rǎdulescu","doi":"10.1007/s00032-021-00348-5","DOIUrl":"https://doi.org/10.1007/s00032-021-00348-5","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46986783","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 : 2022-03-19DOI: 10.1007/s00032-021-00346-7
David P. Kimsey, Matina Trachana
We will consider the multidimensional truncated (p times p) Hermitian matrix-valued moment problem. We will prove a characterisation of truncated (p times p) Hermitian matrix-valued multisequence with a minimal positive semidefinite matrix-valued representing measure via the existence of a flat extension, i.e., a rank preserving extension of a multivariate Hankel matrix (built from the given truncated matrix-valued multisequence). Moreover, the support of the representing measure can be computed via the intersecting zeros of the determinants of matrix-valued polynomials which describe the flat extension. We will also use a matricial generalisation of Tchakaloff’s theorem due to the first author together with the above result to prove a characterisation of truncated matrix-valued multisequences which have a representing measure. When (p = 1), our result recovers the celebrated flat extension theorem of Curto and Fialkow. The bivariate quadratic matrix-valued problem and the bivariate cubic matrix-valued problem are explored in detail.
我们将考虑多维截断(p times p)厄米矩阵值矩问题。我们将通过一个平面扩展的存在性证明截断的(p times p)荷米特矩阵值多序列的一个特征，即多元汉克尔矩阵的一个保秩扩展(从给定的截断的荷米特矩阵值多序列建立)。此外，表示测度的支持度可以通过描述平面扩展的矩阵值多项式的行列式的相交零来计算。我们还将利用第一作者对Tchakaloff定理的一个物质推广，结合上述结果，证明具有表示测度的截断矩阵值多序列的一个表征。当(p = 1)时，我们的结果恢复了Curto和Fialkow著名的平面扩展定理。详细探讨了二元二次矩阵值问题和二元三次矩阵值问题。
{"title":"On a Solution of the Multidimensional Truncated Matrix-Valued Moment Problem","authors":"David P. Kimsey, Matina Trachana","doi":"10.1007/s00032-021-00346-7","DOIUrl":"https://doi.org/10.1007/s00032-021-00346-7","url":null,"abstract":"<p>We will consider the multidimensional truncated <span>(p times p)</span> Hermitian matrix-valued moment problem. We will prove a characterisation of truncated <span>(p times p)</span> Hermitian matrix-valued multisequence with a minimal positive semidefinite matrix-valued representing measure via the existence of a flat extension, i.e., a rank preserving extension of a multivariate Hankel matrix (built from the given truncated matrix-valued multisequence). Moreover, the support of the representing measure can be computed via the intersecting zeros of the determinants of matrix-valued polynomials which describe the flat extension. We will also use a matricial generalisation of Tchakaloff’s theorem due to the first author together with the above result to prove a characterisation of truncated matrix-valued multisequences which have a representing measure. When <span>(p = 1)</span>, our result recovers the celebrated flat extension theorem of Curto and Fialkow. The bivariate quadratic matrix-valued problem and the bivariate cubic matrix-valued problem are explored in detail.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495280","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}
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