Zobrazeno 1 - 10
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pro vyhledávání: '"15A15"'
Autor:
Barry, Paul
We define the triple Riordan group, whose elements consist of $4$-tuples of power series $(g, f_1, f_2, f_3)$ with $g\in \mathbf{R}[[x^3]]$, and $f_1, f_2, f_3 \in x\mathbf{R}[[x^3]]$, for an appropriate ring $\mathbf{R}$. The construction of this gr
Externí odkaz:
http://arxiv.org/abs/2412.05461
We consider polynomials of the form $\operatorname{h}_m(y_1^{[\varkappa_1]},\ldots,y_n^{[\varkappa_n]})$, where $\operatorname{h}_m$ is the complete homogeneous polynomial of degree $m$ and $y_j^{[\varkappa_j]}$ denotes $y_j$ repeated $\varkappa_j$ t
Externí odkaz:
http://arxiv.org/abs/2412.03086
For a given positive integer $m$, the concept of {\it hyperdeterminantal total positivity} is defined for a kernel $K:\R^{2m} \to \R$, thereby generalizing the classical concept of total positivity. Extending the fundamental example, $K(x,y) = \exp(x
Externí odkaz:
http://arxiv.org/abs/2412.03000
Autor:
Vinnikov, Victor, Woerdeman, Hugo J.
We establish various certifying determinantal representation results for a polynomial that contains as a factor a prescribed multivariable polynomials that is strictly stable on a tube domain. The proofs use a Cayley transform in combination with the
Externí odkaz:
http://arxiv.org/abs/2411.17526
The class of strictly sign regular (SSR) matrices has been extensively studied by many authors over the past century, notably by Schoenberg, Motzkin, Gantmacher, and Krein. A classical result of Gantmacher-Krein assures the existence of SSR matrices
Externí odkaz:
http://arxiv.org/abs/2411.14287
Autor:
Chen, Yin, Zhang, Runxuan
The coefficient algebra of a finite-dimensional Lie algebra with respect to a faithful representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We establish a connection between classic
Externí odkaz:
http://arxiv.org/abs/2411.11095
We show that for a multivariable polynomial $p(z)=p(z_1, \ldots , z_d)$ with a determinantal representation $$ p(z) = p(0) \det (I_n- K (\oplus_{j=1}^d z_j I_{n_j}))$$ the matrix $K$ is structurally similar to a strictly $J$-contractive matrix for so
Externí odkaz:
http://arxiv.org/abs/2411.05385
Autor:
Damase, Sujit Sakharam, Khare, Apoorva
Belton-Guillot-Khare-Putinar [J. d'Analyse Math. 2023] classified the post-composition operators that preserve TP/TN kernels of each specified order. We explain how to extend this from preservers to transforms, and from one to several variables. Name
Externí odkaz:
http://arxiv.org/abs/2411.03391
Autor:
Nielsen, Klaus
We classify the bireflections (products of 2 involutions) in the commutator subgroup G an orthogonal group O(V) over a finite field GF(q) of characteristic not 2. We show that every element of G is a bireflection if it is reversible (conjugate to its
Externí odkaz:
http://arxiv.org/abs/2411.01323
A multidimensional nonnegative matrix is called polystochastic if the sum of its entries over each line is equal to $1$. The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. We prove that if $d$ is even, th
Externí odkaz:
http://arxiv.org/abs/2410.09546