کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4603369 1336958 2008 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Twisted inner products and contraction inequalities on spaces of contravariant and covariant tensors
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Twisted inner products and contraction inequalities on spaces of contravariant and covariant tensors
چکیده انگلیسی

Given positive integers n and p, and a complex finite dimensional vector space V, we let Sn,p(V) denote the set of all functions from V×V×⋯×V-(n+p copies) to C that are linear and symmetric in the first n positions, and conjugate linear symmetric in the last p positions. Letting κ=min{n,p} we introduce twisted inner products, [·,·]s,t,1⩽s,t⩽κ, on Sn,p(V), and prove the monotonicity condition [F,F]s,t⩾[F,F]u,v is satisfied when s⩽u⩽κ,t⩽v⩽κ, and F∈Sn,p(V). Using the monotonicity condition, and the Cauchy-Schwartz inequality, we obtain as corollaries many known inequalities involving norms of symmetric multilinear functions, which in turn imply known inequalities involving permanents of positive semidefinite Hermitian matrices. New tensor and permanental inequalities are also presented. Applications to partial differential equations are indicated.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 429, Issue 7, 1 October 2008, Pages 1489-1503