Integral Equations and Operator Theory最新文献_第8页

Minimal Realizations and Determinantal Representations in the Indefinite Setting 不确定环境中的最小实现和决定表示

IF 0.8 3区数学

Integral Equations and Operator Theory Pub Date : 2022-05-06 DOI: 10.1007/s00020-022-02697-1

Joshua D. Jackson, Hugo J. Woerdeman

{"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":"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).","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"72 1","pages":""},"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}

引用次数: 1

Correction to: Weak Product Spaces of Dirichlet Series 对Dirichlet级数的弱乘积空间的修正

IF 0.8 3区数学

Integral Equations and Operator Theory Pub Date : 2022-05-06 DOI: 10.1007/s00020-023-02736-5

Ole Fredrik Brevig, Karl-Mikael Perfekt

引用次数: 1

Invariant Subspaces of Idempotents on Hilbert Spaces Hilbert空间上幂等项的不变子空间

IF 0.8 3区数学

Integral Equations and Operator Theory Pub Date : 2022-04-26 DOI: 10.1007/s00020-022-02723-2

N. Bala, Nirupam Ghosh, J. Sarkar

引用次数: 0

Essential Spectrum and Feller Type Properties 基本光谱和费勒类型属性

IF 0.8 3区数学

Integral Equations and Operator Theory Pub Date : 2022-04-20 DOI: 10.1007/s00020-023-02732-9

A. BenAmor, B. Güneysu, P. Stollmann

引用次数: 0

Feynman’s Operational Calculus with Arbitrary Measures: An Evolution Equation in the General Case and Examples 费曼任意测度算子:一个一般情况下的演化方程及其实例

IF 0.8 3区数学

Integral Equations and Operator Theory Pub Date : 2022-04-16 DOI: 10.1007/s00020-022-02694-4

L. Nielsen

引用次数: 1

Norms of Basic Operators in Vector Valued Model Spaces and de Branges Spaces 向量值模型空间和de brange空间中基本算子的范数

IF 0.8 3区数学

Integral Equations and Operator Theory Pub Date : 2022-03-11 DOI: 10.1007/s00020-022-02719-y

Kousik Dhara, H. Dym

引用次数: 0

Commutative Algebras of Toeplitz Operators on the Bergman Space Revisited: Spectral Theorem Approach Bergman空间上Toeplitz算子的交换代数:谱定理方法

IF 0.8 3区数学

Integral Equations and Operator Theory Pub Date : 2022-03-08 DOI: 10.1007/s00020-022-02706-3

G. Rozenblum, N. Vasilevski

引用次数: 74

An Interpersonal Approach to the Treatment of Social Anxiety Disorder (Social Phobia): A Component Analysis. 人际交往法治疗社交焦虑症（社交恐惧症）：成分分析。

IF 0.7 3区数学

Integral Equations and Operator Theory Pub Date : 2022-03-01 DOI: 10.5152/pcp.2022.21246

Ariel Stravynski, Lise Lachance

{"title":"An Interpersonal Approach to the Treatment of Social Anxiety Disorder (Social Phobia): A Component Analysis.","authors":"Ariel Stravynski, Lise Lachance","doi":"10.5152/pcp.2022.21246","DOIUrl":"10.5152/pcp.2022.21246","url":null,"abstract":"Background: Most treatments of social anxiety disorder aim at anxiety reduction. To what extent this leads to improved social functioning remains unclear. An effective alternative aiming primarily at social functioning- the Interpersonal Approach- is available. The present study sought to identify its active ingredients.Methods: This is a randomized controlled study; 102 social anxiety disorder individuals were randomly assigned to 3 versions of the Interpersonal Approach. A total of 76 patients completed treatment and 67, a 1-year follow-up. The patients met Diagnostic and Statistical Manual of Mental Disorders, fourth edition criteria for social anxiety disorder. The study was carried out in an experimental clinic for the treatment of social anxiety disorder at the Research Center of Louis-H. Lafontaine Hospital in Montreal, Canada.Results: No clinically meaningful change occurred during the waiting list. A significant and equivalent improvement was obtained in all treatment conditions in social functioning, anxiousness, and general psychopathology, maintaining over a 12-month follow-up. Remission rates improved progressively with 54% remission at 1-year follow-up. All variants of the Interpersonal Approach resulted in similar improvements.Conclusion: The Interpersonal Approach in all its versions has proved to be effective in reducing anxiety complaints and improving social functioning. The combined improvement in these 2 outcomes accounts for the significant remission rates seen at 1-year follow-up. Two active features were common to all: (1) targeting and ultimately dissolving long-standing habits of self-protection across various spheres of life and (2) fostering participatory interpersonal patterns of behavior, enacted by patients systematically and repeatedly between sessions.","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"15 1","pages":"33-44"},"PeriodicalIF":0.7,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11099670/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73092757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Limit Laws for R-diagonal Variables in a Tracial Probability Space 循迹概率空间中r -对角变量的极限律

IF 0.8 3区数学

Integral Equations and Operator Theory Pub Date : 2022-02-21 DOI: 10.1007/s00020-022-02689-1

Cong Zhou

引用次数: 1

Coupled Domain-Boundary Variational Formulations for Hodge–Helmholtz Operators Hodge-Helmholtz算子的耦合域边界变分公式

IF 0.8 3区数学

Integral Equations and Operator Theory Pub Date : 2022-02-03 DOI: 10.1007/s00020-022-02684-6

Erick Schulz, R. Hiptmair

引用次数: 2