Publications of Branko Ćurgus

There are five groups of publications below: submitted, peer reviewed, invited , theses , and published only on this website .

Submitted for publication in peer reviewed journals
  1. Stability of roots of polynomials under linear combinations of derivatives. (with Vania Mascioni)
  2. Somewhat stochastic matrices. (with Robert I. Jewett)
    In this paper the standard theorem for regular stochastic matrices is generalized to matrices with no sign restriction on the entries. The condition that column sums be equal to $1$ is kept, but the regularity condition is replaced by a condition on the $\ell_1$-distances between columns.

  3. Riesz basis of root vectors of indefinite Sturm-Liouville problems with eigenparameter dependent boundary conditions, II. (with Paul Binding)
    Detailed calculations for the opening example in this paper can be found here.

Peer reviewed publications

  1. On a convex operator for finite sets. (with Krzysztof Kołodziejczyk). Discrete Applied Mathematics 155 (2007) no. 13, 1774--1792.
    In this paper we introduce a convex operator which generalizes the familiar concepts of the convex hull and the affine hull of a finite set of points. We call this operator a convex interval hull. For example, this operator, with a special choice of intervals, assigns a regular dodecagon to the 4-element set consisting of the vertices and the orthocenter of an equilateral triangle. For another choice of intervals, the operator assigns an equilateral triangle to the same set of points. The transition from the triangle to the dodecagon, changing one interval at each step, is presented in the animation. The specific intervals are given in the paper on page 5.
    Click to enlarge

  2. Root preserving transformations of polynomials. (with Vania Mascioni) Mathematics Magazine 80 (2007) no. 2, 136--138.
  3. Perturbations of roots under linear transformations of polynomials. (with Vania Mascioni) Constructive Approximation 25 (2007), no. 3, 255--277.
  4. An unexpected limit of expected values. (with Robert I. Jewett) Expositiones Mathematicae 25 (2007), no. 1, 1--20.
  5. An exceptional exponential function. The College Mathematics Journal 37 (2006), no. 5, 344--354.
  6. Riesz basis of root vectors of indefinite Sturm-Liouville problems with eigenparameter dependent boundary conditions, I. (with Paul Binding) in Operator Theory and Indefinite Inner Product Spaces, The Proceedings of the Colloquium held on the occasion of the retirement of Heinz Langer, Vienna, Austria. 75--96, Operator Theory: Advances and Applications, Vol. 163, Birkhäuser, 2006.
  7. Roots and polynomials as homeomorphic spaces. (with Vania Mascioni) Expositiones Mathematicae 24 (2006), no. 1, 81--95.
  8. A counterexample in Sturm-Liouville completeness theory. (with P. Binding) Proceedings of the Royal Society of Edinburgh: Section A: Mathematics 134 (2004), no. 2, 241--248.
  9. A contraction of the Lucas polygon. (with V. Mascioni) Proceedings of the American Mathematical Society 132 (2004), no. 10, 2973--2981.
  10. Continuous embeddings, completions and complementation in Krein spaces. (with H. Langer) Radovi Matematički 12 (2003), no. 1, 37--79.
  11. Standard symmetric operators in Pontryagin spaces: A generalized von Neumann formula and minimality of boundary coefficients. (with T. Azizov and A. Dijksma) Journal of Functional Analysis 198 (2003), no. 2, 361--412.
  12. On the location of critical points of polynomials. (with V. Mascioni) Proceedings of the American Mathematical Society 131 (2003), no. 1, 253--264.
  13. Form domains and eigenfunction expansions for differential equations with eigenparameter dependent boundary conditions. (with P. Binding) Canadian Journal of Mathematics 54 (2002), no. 6, 1142--1164.
  14. Discreteness of the spectrum of second order differential operators and associated embedding theorems. (with T. T. Read) Journal of Differential Equations, 184 (2002), no. 2, 526--548.
  15. The linearization of boundary eigenvalue problems and reproducing kernel Hilbert spaces. (with A. Dijksma and T. T. Read) Linear Algebra and its Applications. 329 (2001), no. 1-3, 97--136.
  16. On singular critical points of positive operators in Krein spaces. (with A. Gheondea and H. Langer) Proceedings of the American Mathematical Society 128 (2000), no. 9, 2621--2626.
  17. Boundary value problems in Krein spaces. Dedicated to the memory of Branko Najman. Glasnik Matematički Ser. III 35(55) (2000), no. 1, 45--58.
  18. Positive differential operators in Krein space $L^{2}({\mathbb R}^n)$. (with B. Najman) Contributions to Operator Theory in Spaces with an Indefinite Metric, The Heinz Langer Anniversary Volume, 113--129, Edited by A. Dijksma, I. Gohberg, M. A. Kaashoek, and R. Mennicken. Operator Theory: Advances and Applications, Vol. 106, Birkhäuser, 1998.
  19. Examples of positive operators in Krein space with $0$ a regular critical point of infinite rank. (with B. Najman), 51--56, Operator Theory: Advances and Applications, Vol. 102, Birkhäuser, Basel, 1998.
  20. Preservation of the range under perturbations of an operator. (with B. Najman) Proceedings of the American Mathematical Society 125 (1997), no. 9, 2627--2631.
  21. Positive differential operators in Krein space $L^{2}({\mathbb R})$. (with B. Najman) Recent developments in operator theory and its applications (Winnipeg, MB, 1994), 95--104, Operator Theory: Advances and Applications, Vol. 87, Birkhäuser, Basel, 1996.
  22. Quadratic eigenvalue problems. (with B. Najman) Mathematische Nachrichten 174 (1995), 55--64.
  23. Quasi-uniformly positive operators in Krein space. (with B. Najman) Operator theory and boundary eigenvalue problems (Vienna, 1993), 90--99, Operator Theory: Advances and Applications, Vol. 80, Birkhäuser, Basel, 1995.
  24. The operator $(\mbox{sgn}\,x)\frac{d^{2}}{dx^{2}}$ is similar to a self-adjoint operator in $L^{2}({\mathbb R})$. (with B. Najman) Proceedings of the American Mathematical Society 123 (1995), no. 4, 1125--1128.
  25. A Krein space approach to elliptic eigenvalue problems with indefinite weights. (with B. Najman) Differential and Integral Equations 7 (1994), no. 5-6, 1241--1252.
  26. Definitizable extensions of positive symmetric operators in a Krein space. Integral Equations and Operator Theory 12 (1989), no. 5, 615--631.
  27. Characteristic functions of unitary colligations and bounded operators in Krein spaces. (with A. Dijksma, H. Langer, H.S.V. de Snoo) in The Gohberg Anniversary Collection, Vol. II, 125--152, Edited by H. Dym, S. Goldberg, M. A. Kaashoek, P. Lancaster, Operator Theory: Advances and Applications, Vol. 41, Birkhäuser Verlag, Basel, (1989).
  28. A Krein space approach to symmetric ordinary differential operators with an indefinite weight function. (with H. Langer) Journal of Differential Equations 79 (1989), no. 1, 31--61.
  29. On the regularity of the critical point infinity of definitizable operators. Integral Equations and Operator Theory 8 (1985), no. 4, 462--488.
  30. Nonmeasurable sets and pairs of transfinite sequences. (with H. I. Miller) Akad. Nauka Umjet. Bosne Hercegov. Rad. Odjelj. Prirod. Mat. Nauka LXIX (1982), 39--43.

Invited publications

  1. Numbers in the Sky(viewing Sculpture). Isamu Noguchi and Skyviewing Sculpture. Proceeding of symposia and special lectures. Edited by Sarah Clark-Langager and Michiko Yusa, Western Washington University, Bellingham, Wahington, (2004), 75--82.
  2. Spectral properties of self-adjoint ordinary differential operators with an indefinite weight function. (with H. Langer) Proceedings of the 1984 Workshop ``Spectral theory of Sturm-Liouville differential operators,'' ANL-84-73, Argonne National Laboratory, Argonne, Ill., (1984), 73--80.

Theses

  1. Definitizable operators in Krein spaces. Applications to ordinary self-adjoint differential operators with an indefinite weight function. ( Serbo-Croatian) PhD thesis. University of Sarajevo, 1985.
  2. Spectral theorem for definitizable $J$-unitary and $J$-self-adjoint operators. ( Serbo-Croatian) Master thesis. University of Sarajevo, 1984.

Papers published only on this website

  1. On the variation of $3\!\times\!3$ stochastic matrices. A computer generated proof of a claim in Example 6.3 in the paper "Somewhat stochastic matrices". (with Robert I. Jewett)
Last updated: August 2, 2008.