Zobrazeno 1 - 10
of 82
pro vyhledávání: '"Borcea, Julius"'
Autor:
Borcea, Julius, Brändén, Petter
Publikováno v:
C. R. Math. Acad. Sci. Paris 348 (2010), no. 15-16, 843-846
The majorization order on $\RR^n$ induces a natural partial ordering on the space of univariate hyperbolic polynomials of degree $n$. We characterize all linear operators on polynomials that preserve majorization, and show that it is sufficient (modu
Externí odkaz:
http://arxiv.org/abs/1005.5293
We study subharmonic functions whose Laplacian is supported on a null set and in connected components of of the complement to the support admit harmonic extensions to larger sets. We prove that if such a function has a piecewise holomorphic derivativ
Externí odkaz:
http://arxiv.org/abs/0912.4650
Autor:
Borcea, Julius
We characterize all linear operators on finite or infinite-dimensional spaces of univariate real polynomials preserving the sets of elliptic, positive, and non-negative polynomials, respectively. This is done by means of Fischer-Fock dualities, Hanke
Externí odkaz:
http://arxiv.org/abs/0811.4374
Autor:
Borcea, Julius, Brändén, Petter
Publikováno v:
Lett. Math. Phys. 86 (2008), 53-61
We describe all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing in open circular domains. This completes the multivariate generalization of the classification program initiated by P\'olya-Schur fo
Externí odkaz:
http://arxiv.org/abs/0810.1007
Autor:
Borcea, Julius, Brändén, Petter
Publikováno v:
Comm. Pure Appl. Math. 62 (2009), no. 12, 1595-1631
In the first part of this series we characterized all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing in products of open circular domains. For such sets this completes the multivariate generaliza
Externí odkaz:
http://arxiv.org/abs/0809.3087
Autor:
Borcea, Julius, Brändén, Petter
Publikováno v:
Invent. Math. 177 (2009), no. 3, 541-569
In 1952 Lee and Yang proposed the program of analyzing phase transitions in terms of zeros of partition functions. Linear operators preserving non-vanishing properties are essential in this program and various contexts in complex analysis, probabilit
Externí odkaz:
http://arxiv.org/abs/0809.0401
Following the classical approach of P\'olya-Schur theory we initiate in this paper the study of linear operators acting on $\mathbb{R}[x]$ and preserving either the set of positive univariate polynomials or similar sets of non-negative and elliptic p
Externí odkaz:
http://arxiv.org/abs/0801.1749
Given a $(k+1)$-tuple $A, B_1,...,B_k$ of $(m\times n)$-matrices with $m\le n$ we call the set of all $k$-tuples of complex numbers $\{\la_1,...,\la_k\}$ such that the linear combination $A+\la_1B_1+\la_2B_2+...+\la_kB_k$ has rank smaller than $m$ th
Externí odkaz:
http://arxiv.org/abs/0711.3609
Publikováno v:
J. Amer. Math. Soc. 22 (2009), 521-567.
We introduce the class of {\em strongly Rayleigh} probability measures by means of geometric properties of their generating polynomials that amount to the stability of the latter. This class covers important models such as determinantal measures (e.g
Externí odkaz:
http://arxiv.org/abs/0707.2340
Consider a homogenized spectral pencil of exactly solvable linear differential operators $T_{\la}=\sum_{i=0}^k Q_{i}(z)\la^{k-i}\frac {d^i}{dz^i}$, where each $Q_{i}(z)$ is a polynomial of degree at most $i$ and $\la$ is the spectral parameter. We sh
Externí odkaz:
http://arxiv.org/abs/0705.2822