Bilinear Forms and Zonal Polynomials

1995 ◽  
Author(s):  
A. M. Mathai ◽  
Serge B. Provost ◽  
Takesi Hayakawa
Keyword(s):  
Bilinear Forms ◽  
Zonal Polynomials

scholarly journals Nonsingular bilinear forms on direct sums of ideals

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Beata Rothkegel
Keyword(s):  
Bilinear Form ◽  
Dedekind Domain ◽  
Bilinear Forms ◽  
Direct Sums ◽  
Direct Sum

AbstractIn the paper we formulate a criterion for the nonsingularity of a bilinear form on a direct sum of finitely many invertible ideals of a domain. We classify these forms up to isometry and, in the case of a Dedekind domain, up to similarity.

scholarly journals EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS

2021 ◽  
pp. 1-66
Author(s):  
Tom Bachmann ◽  
Kirsten Wickelgren
Keyword(s):  
Commutative Algebra ◽  
Vector Bundles ◽  
Euler Class ◽  
Complete Intersections ◽  
Bilinear Forms ◽  
Euler Numbers ◽  
Coherent Sheaves ◽  
Linear Subspaces ◽  
Algebraic Vector

Abstract We equate various Euler classes of algebraic vector bundles, including those of [12] and one suggested by M. J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class and give formulas for local indices at isolated zeros, both in terms of the six-functors formalism of coherent sheaves and as an explicit recipe in the commutative algebra of Scheja and Storch. As an application, we compute the Euler classes enriched in bilinear forms associated to arithmetic counts of d-planes on complete intersections in $\mathbb P^n$ in terms of topological Euler numbers over $\mathbb {R}$ and $\mathbb {C}$ .

Bilinear forms on non-homogeneous Sobolev spaces

2020 ◽  
Vol 32 (4) ◽  
pp. 995-1026
Author(s):  
Carme Cascante ◽  
Joaquín M. Ortega
Keyword(s):  
Sobolev Spaces ◽  
Bilinear Form ◽  
Positive Measure ◽  
Bilinear Forms ◽  
Homogeneous Sobolev Spaces

AbstractIn this paper, we show that if {b\in L^{2}(\mathbb{R}^{n})}, then the bilinear form defined on the product of the non-homogeneous Sobolev spaces {H_{s}^{2}(\mathbb{R}^{n})\times H_{s}^{2}(\mathbb{R}^{n})}, {0<s<1}, by(f,g)\in H_{s}^{2}(\mathbb{R}^{n})\times H_{s}^{2}(\mathbb{R}^{n})\to\int_{% \mathbb{R}^{n}}(\mathrm{Id}-\Delta)^{\frac{s}{2}}(fg)(\mathbf{x})b(\mathbf{x})% \mathop{}\!d\mathbf{x}is continuous if and only if the positive measure {\lvert b(\mathbf{x})\rvert^{2}\mathop{}\!d\mathbf{x}} is a trace measure for {H_{s}^{2}(\mathbb{R}^{n})}.

Polarization Relations and Dispersion Equations for Anisotropic Moving Media

1979 ◽  
Vol 34 (10) ◽  
pp. 1147-1157 ◽  
Author(s):  
Helmut Hebenstreit ◽  
Kurt Suchy
Keyword(s):  
Quadratic Forms ◽  
Bilinear Forms ◽  
Dispersion Equations ◽  
Left And Right ◽  
Moving Media ◽  
Eigenvectors And Eigenvalues

Abstract For media anisotropic (but not bi-anisotropic) in the comoving frame polarization relations and dispersion equations are derived using bilinear forms and quadratic forms, respectively. Specializations for media electrically anisotropic but magnetically isotropic (or vice versa) are given using (left and right) eigenvectors and eigenvalues of the material tensors.

Some criteria for nuclearity

1986 ◽  
Vol 100 (1) ◽  
pp. 151-159 ◽  
Author(s):  
M. A. Sofi
Keyword(s):  
Sequence Space ◽  
Convex Space ◽  
Locally Convex Space ◽  
Sequence Spaces ◽  
Bilinear Forms ◽  
Simple Formulation ◽  
Normal Topology ◽  
Nuclear Spaces ◽  
Locally Convex

For a given locally convex space, it is always of interest to find conditions for its nuclearity. Well known results of this kind – by now already familiar – involve the use of tensor products, diametral dimension, bilinear forms, generalized sequence spaces and a host of other devices for the characterization of nuclear spaces (see [9]). However, it turns out, these nuclearity criteria are amenable to a particularly simple formulation in the setting of certain sequence spaces; an elegant example is provided by the so-called Grothendieck–Pietsch (GP, for short) criterion for nuclearity of a sequence space (in its normal topology) in terms of the summability of certain numerical sequences.

Bilinear forms of Coxeter systems

2001 ◽  
pp. 75-80
Author(s):  
Richard Kane ◽  
Jonathan Borwein ◽  
Peter Borwein
Keyword(s):  
Bilinear Forms ◽  
Coxeter Systems

Bilinear Forms

1977 ◽  
pp. 89-124 ◽  
Author(s):  
K. W. Gruenberg ◽  
A. J. Weir
Keyword(s):  
Bilinear Forms

Adaptive filtering for the identification of bilinear forms

2018 ◽  
Vol 75 ◽  
pp. 153-167 ◽  
Author(s):  
Constantin Paleologu ◽  
Jacob Benesty ◽  
Silviu Ciochină
Keyword(s):  
Adaptive Filtering ◽  
Bilinear Forms
Sign in / Sign up

Export Citation Format

Share Document