Pub Date : 2022-06-06DOI: 10.1007/s00020-022-02720-5
Georgios Tsikalas
{"title":"Subinner-Free Outer Factorizations on an Annulus","authors":"Georgios Tsikalas","doi":"10.1007/s00020-022-02720-5","DOIUrl":"https://doi.org/10.1007/s00020-022-02720-5","url":null,"abstract":"","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41996249","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 : 2022-05-28DOI: 10.1007/s00020-022-02701-8
B. Wick, Shengkun Wu
{"title":"Integral Operators on Fock–Sobolev Spaces via Multipliers on Gauss–Sobolev Spaces","authors":"B. Wick, Shengkun Wu","doi":"10.1007/s00020-022-02701-8","DOIUrl":"https://doi.org/10.1007/s00020-022-02701-8","url":null,"abstract":"","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52032658","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 : 2022-05-28DOI: 10.1007/s00020-022-02703-6
Steven Redolfi, R. Weikard
{"title":"Green’s Functions for First-Order Systems of Ordinary Differential Equations without the Unique Continuation Property","authors":"Steven Redolfi, R. Weikard","doi":"10.1007/s00020-022-02703-6","DOIUrl":"https://doi.org/10.1007/s00020-022-02703-6","url":null,"abstract":"","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52032671","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 : 2022-05-06DOI: 10.1007/s00020-022-02696-2
Senhua Zhu, Yufeng Lu, Yixin Yang
In this paper, we study the Agler reducing subspace for the compressed shift on the Beurling type quotient module (mathcal {K}_{Theta }) over the bidisk, where (Theta ) is an operator-valued inner function. Firstly, we characterized the Agler reducing subspace when (Theta ) is an one variable operator-valued inner function, which is quite different with the scalar setting. Secondly, we show that the compressed shift has nontrivial Agler reducing subspaces if and only if (Theta ) is the product of two one variable inner fucntions(though now the order of the factors plays a role). The uniqueness of the Agler reducing subspace is also studied.
{"title":"The Agler Reducing Subspace for the Operator-Valued Inner Function Over the Bidisk","authors":"Senhua Zhu, Yufeng Lu, Yixin Yang","doi":"10.1007/s00020-022-02696-2","DOIUrl":"https://doi.org/10.1007/s00020-022-02696-2","url":null,"abstract":"<p>In this paper, we study the Agler reducing subspace for the compressed shift on the Beurling type quotient module <span>(mathcal {K}_{Theta })</span> over the bidisk, where <span>(Theta )</span> is an operator-valued inner function. Firstly, we characterized the Agler reducing subspace when <span>(Theta )</span> is an one variable operator-valued inner function, which is quite different with the scalar setting. Secondly, we show that the compressed shift has nontrivial Agler reducing subspaces if and only if <span>(Theta )</span> is the product of two one variable inner fucntions(though now the order of the factors plays a role). The uniqueness of the Agler reducing subspace is also studied.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516117","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 : 2022-05-06DOI: 10.1007/s00020-022-02698-0
Javad Mashreghi, Pierre-Olivier Parisé, Thomas Ransford
We show that there exists a de Branges–Rovnyak space ({mathcal {H}}(b)) on the unit disk containing a function f with the following property: even though f can be approximated by polynomials in ({mathcal {H}}(b)), neither the Taylor partial sums of f nor their Cesàro, Abel, Borel or logarithmic means converge to f in ({mathcal {H}}(b)). A key tool is a new abstract result showing that, if one regular summability method includes another for scalar sequences, then it automatically does so for certain Banach-space-valued sequences too.
{"title":"Power-Series Summability Methods in de Branges–Rovnyak Spaces","authors":"Javad Mashreghi, Pierre-Olivier Parisé, Thomas Ransford","doi":"10.1007/s00020-022-02698-0","DOIUrl":"https://doi.org/10.1007/s00020-022-02698-0","url":null,"abstract":"<p>We show that there exists a de Branges–Rovnyak space <span>({mathcal {H}}(b))</span> on the unit disk containing a function <i>f</i> with the following property: even though <i>f</i> can be approximated by polynomials in <span>({mathcal {H}}(b))</span>, neither the Taylor partial sums of <i>f</i> nor their Cesàro, Abel, Borel or logarithmic means converge to <i>f</i> in <span>({mathcal {H}}(b))</span>. A key tool is a new abstract result showing that, if one regular summability method includes another for scalar sequences, then it automatically does so for certain Banach-space-valued sequences too.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516111","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 : 2022-05-06DOI: 10.1007/s00020-022-02697-1
Joshua D. Jackson, Hugo J. Woerdeman
For a signature matrix J, we show that a rational matrix function M(z) that is strictly J-contractive on the unit circle ({{mathbb {T}}}), has a strict ({tilde{J}}oplus J)-contractive realization (begin{bmatrix} A &{} B C &{} D end{bmatrix}) for an appropriate signature matrix ({tilde{J}}); that is, ( M(z) = D +zC (I -zA)^{-1} B ). As an application, we use this result to show that a two variable polynomial (p(z_1,z_2)) of degree ((n_1,n_2)), (n_2=1), without roots on ({ (0,0) } cup ({{mathbb {T}}} times { 0 } ) cup {{mathbb {T}}}^2) allows a determinantal representation
$$begin{aligned} p(z_1, z_2) = p(0,0) det (I_{n_1+1} - K Z), Z = z_1 I_{n_1} oplus z_2 I_{n_2} , end{aligned}$$(1)
where K is a strict ({tilde{J}}oplus J)-contraction. This provides first evidence of a new conjecture that a two variable polynomial (p(z_1,z_2)) of degree ((n_1,n_2)) has a determinantal representation (1) with K a strict ({tilde{J}}oplus J)-contraction if and only if (p(z_1,z_2)) has no roots in ({ (0,0) } cup {{mathbb {T}}}^2).
对于一个签名矩阵J，我们证明了一个在单位圆({{mathbb {T}}})上严格J压缩的有理矩阵函数M(z)对于一个合适的签名矩阵({tilde{J}})具有严格({tilde{J}}oplus J) -压缩实现(begin{bmatrix} A &{} B C &{} D end{bmatrix});也就是( M(z) = D +zC (I -zA)^{-1} B )。作为一个应用，我们用这个结果来证明一个二阶多项式(p(z_1,z_2))的次为((n_1,n_2)), (n_2=1)，在({ (0,0) } cup ({{mathbb {T}}} times { 0 } ) cup {{mathbb {T}}}^2)上没有根允许一个行列式表示$$begin{aligned} p(z_1, z_2) = p(0,0) det (I_{n_1+1} - K Z), Z = z_1 I_{n_1} oplus z_2 I_{n_2} , end{aligned}$$(1)，其中K是一个严格的({tilde{J}}oplus J) -收缩。这提供了一个新猜想的第一个证据，即次为((n_1,n_2))的两个变量多项式(p(z_1,z_2))具有行列式表示(1)，其中K是严格的({tilde{J}}oplus J) -收缩，当且仅当(p(z_1,z_2))在({ (0,0) } cup {{mathbb {T}}}^2)中没有根。
{"title":"Minimal Realizations and Determinantal Representations in the Indefinite Setting","authors":"Joshua D. Jackson, Hugo J. Woerdeman","doi":"10.1007/s00020-022-02697-1","DOIUrl":"https://doi.org/10.1007/s00020-022-02697-1","url":null,"abstract":"<p>For a signature matrix <i>J</i>, we show that a rational matrix function <i>M</i>(<i>z</i>) that is strictly <i>J</i>-contractive on the unit circle <span>({{mathbb {T}}})</span>, has a strict <span>({tilde{J}}oplus J)</span>-contractive realization <span>(begin{bmatrix} A &{} B C &{} D end{bmatrix})</span> for an appropriate signature matrix <span>({tilde{J}})</span>; that is, <span>( M(z) = D +zC (I -zA)^{-1} B )</span>. As an application, we use this result to show that a two variable polynomial <span>(p(z_1,z_2))</span> of degree <span>((n_1,n_2))</span>, <span>(n_2=1)</span>, without roots on <span>({ (0,0) } cup ({{mathbb {T}}} times { 0 } ) cup {{mathbb {T}}}^2)</span> allows a determinantal representation </p><span>$$begin{aligned} p(z_1, z_2) = p(0,0) det (I_{n_1+1} - K Z), Z = z_1 I_{n_1} oplus z_2 I_{n_2} , end{aligned}$$</span>(1)<p>where <i>K</i> is a strict <span>({tilde{J}}oplus J)</span>-contraction. This provides first evidence of a new conjecture that a two variable polynomial <span>(p(z_1,z_2))</span> of degree <span>((n_1,n_2))</span> has a determinantal representation (1) with <i>K</i> a strict <span>({tilde{J}}oplus J)</span>-contraction if and only if <span>(p(z_1,z_2))</span> has no roots in <span>({ (0,0) } cup {{mathbb {T}}}^2)</span>.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516100","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 : 2022-05-06DOI: 10.1007/s00020-023-02736-5
Ole Fredrik Brevig, Karl-Mikael Perfekt
{"title":"Correction to: Weak Product Spaces of Dirichlet Series","authors":"Ole Fredrik Brevig, Karl-Mikael Perfekt","doi":"10.1007/s00020-023-02736-5","DOIUrl":"https://doi.org/10.1007/s00020-023-02736-5","url":null,"abstract":"","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43385659","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 : 2022-04-26DOI: 10.1007/s00020-022-02723-2
N. Bala, Nirupam Ghosh, J. Sarkar
{"title":"Invariant Subspaces of Idempotents on Hilbert Spaces","authors":"N. Bala, Nirupam Ghosh, J. Sarkar","doi":"10.1007/s00020-022-02723-2","DOIUrl":"https://doi.org/10.1007/s00020-022-02723-2","url":null,"abstract":"","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47887256","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 : 2022-04-20DOI: 10.1007/s00020-023-02732-9
A. BenAmor, B. Güneysu, P. Stollmann
{"title":"Essential Spectrum and Feller Type Properties","authors":"A. BenAmor, B. Güneysu, P. Stollmann","doi":"10.1007/s00020-023-02732-9","DOIUrl":"https://doi.org/10.1007/s00020-023-02732-9","url":null,"abstract":"","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41738357","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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