Wiener algebra for the quaternions

We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-L\'evy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener-Hopf operators

On the class SI of J-contractive functions intertwining solutions of linear differential equations

In the PhD thesis of the second author under the supervision of the third author was defined the class SI of J-contractive functions, depending on a parameter and arising as transfer functions of overdetermined conservative 2D systems invariant in one direction. In this paper we extend and solve in the class SI, a number of problems originally set for the class SC of functions contractive in the open right-half plane, and unitary on the imaginary line with respect to some preassigned signature matrix J. The problems we consider include the Schur algorithm, the partial realization problem and the Nevanlinna-Pick interpolation problem. The arguments rely on a correspondence between elements in a given subclass of SI and elements in SC. Another important tool in the arguments is a new result pertaining to the classical tangential Schur algorithm.Comment: 46 page

Generalized Fock spaces and the Stirling numbers

The Bargmann-Fock-Segal space plays an important role in mathematical physics, and has been extended into a number of directions. In the present paper we imbed this space into a Gelfand triple. The spaces forming the Fr\'echet part (i.e. the space of test functions) of the triple are characterized both in a geometric way and in terms of the adjoint of multiplication by the complex variable, using the Stirling numbers of the second kind. The dual of the space of test functions has a topological algebra structure, of the kind introduced and studied by the first named author and G. Salomon.Comment: revised versio

Intestinal obstruction due to ileal metastasis of Ewing’s sarcoma

We present a case report of intestinal obstruction caused by ileal metastasis of Ewing’s sarcoma. The invasive tumoral segment of the ileum was removed and the bowel continuity was provided with end-to-end anastomosis. Histopathologic examination showed tumoral invasion of the ileal mucosa and ileal wall by small blue round cells of Ewing’s sarcoma.Keywords: Ewing’s sarcoma, ileal metastasis, intestinal obstructio

Bitangential interpolation in generalized Schur classes

Bitangential interpolation problems in the class of matrix valued functions in the generalized Schur class are considered in both the open unit disc and the open right half plane, including problems in which the solutions is not assumed to be holomorphic at the interpolation points. Linear fractional representations of the set of solutions to these problems are presented for invertible and singular Hermitian Pick matrices. These representations make use of a description of the ranges of linear fractional transformations with suitably chosen domains that was developed in a previous paper.Comment: Second version, corrected typos, changed subsection 5.6, 47 page

Abscess in Adenomyosis Mimicking a Malignancy in a 54-Year-Old Woman

Background: Although there are a few reports describing abscess formation in endometriotic foci no report of abscess formation arising de novo within adenomyosis appears in the literature. Preoperative diagnosis of adenomyosis is frequently difficult because of non-specific signs and symptoms. Synchronous pelvic pathologies such as leiomyoma, endometrial polyp, endometrial hyperplasia, as well as endometrial cancer may cause differential diagnostic problems. Case: A 54-year-old postmenopausal woman complaining of inguinal pain, nightsweats and hot flashes is presented. Radiologic examinations of the pelvis revealed a 95 × 85 mm leiomyoma-like lesion including a 53 × 43 mmcystic space and 9 × 6 mmpapillary formation within the uterus raising clinical suspicion of malignancy. A total abdominal hysterectomy and bilateral salpingo-oophorectomy were performed accompanied by a frozen section diagnosis. The frozen section revealed an abscess formation arising in a focus of adenomyosis. The postoperative period of the patient was uneventful. Conclusion : The present case, to our knowledge, is the first report representing abscess formation in adenomyosis. Abscess arising within adenomyosis can strongly raise the suspicion of endometrial cancer, particularly if the patient is postmenopausal. If endometrial cancer cannot be ruled out with definitive histopathological diagnosis in the preoperative period, a frozen section becomes mandatory during surgical intervention

de Branges-Rovnyak spaces: basics and theory

For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$ and related extension space ${\mathcal D(S)}$ consisting of pairs of analytic functions on the unit disk ${\mathbb D}$. This survey describes three equivalent formulations (the original geometric de Branges-Rovnyak definition, the Toeplitz operator characterization, and the characterization as a reproducing kernel Hilbert space) of the de Branges-Rovnyak space ${\mathcal H}(S)$, as well as its role as the underlying Hilbert space for the modeling of completely non-isometric Hilbert-space contraction operators. Also examined is the extension of these ideas to handle the modeling of the more general class of completely nonunitary contraction operators, where the more general two-component de Branges-Rovnyak model space ${\mathcal D}(S)$ and associated overlapping spaces play key roles. Connections with other function theory problems and applications are also discussed. More recent applications to a variety of subsequent applications are given in a companion survey article

Thermodynamic theory of epitaxial ferroelectric thin films with dense domain structures

A Landau-Ginsburg-Devonshire-type nonlinear phenomenological theory is presented, which enables the thermodynamic description of dense laminar polydomain states in epitaxial ferroelectric thin films. The theory explicitly takes into account the mechanical substrate effect on the polarizations and lattice strains in dissimilar elastic domains (twins). Numerical calculations are performed for PbTiO3 and BaTiO3 films grown on (001)-oriented cubic substrates. The "misfit strain-temperature" phase diagrams are developed for these films, showing stability ranges of various possible polydomain and single-domain states. Three types of polarization instabilities are revealed for polydomain epitaxial ferroelectric films, which may lead to the formation of new polydomain states forbidden in bulk crystals. The total dielectric and piezoelectric small-signal responses of polydomain films are calculated, resulting from both the volume and domain-wall contributions. For BaTiO3 films, strong dielectric anomalies are predicted at room temperature near special values of the misfit strain.Comment: 19 pages, 8 figure

Inverse spectral problems for Dirac operators with summable matrix-valued potentials

We consider the direct and inverse spectral problems for Dirac operators on $(0,1)$ with matrix-valued potentials whose entries belong to $L_p(0,1)$, $p\in[1,\infty)$. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest a method for reconstructing the potential from the corresponding spectral data.Comment: 32 page