منابع مشابه
On constant products of elements in skew polynomial rings
Let $R$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $R$ and $f(X)=a_0+a_1X+cdots+a_nX^n$ be a nonzero skew polynomial in $R[X;alpha]$. It is proved that if there exists a nonzero skew polynomial $g(X)=b_0+b_1X+cdots+b_mX^m$ in $R[X;alpha]$ such that $g(X)f(X)=c$ is a constant in $R$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $R$ such tha...
متن کاملResults on Singular Distribution Products of Mikusiński Type
Results on products of Schwartz distributions are obtained when they have coinciding point singularities and only sums of the products exist in the distribution space. These results follow the pattern of a well-know distributional product published by Jan Mikusiński in 1966, and are named Mikusiński type products. The formulas are derived as the distributions are embedded in Colombeau algebra o...
متن کاملon constant products of elements in skew polynomial rings
let $r$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $r$ and $f(x)=a_0+a_1x+cdots+a_nx^n$ be a nonzero skew polynomial in $r[x;alpha]$. it is proved that if there exists a nonzero skew polynomial $g(x)=b_0+b_1x+cdots+b_mx^m$ in $r[x;alpha]$ such that $g(x)f(x)=c$ is a constant in $r$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $r$ such tha...
متن کاملOn Constructing Matrices with Prescribed Singular Values and Diagonal Elements
Similar to the well known Schur Horn theorem that characterizes the relationship between the diagonal entries and the eigenvalues of a Hermitian matrix the Sing Thompson theorem characterizes the relationship between the diagonal en tries and the singular values of an arbitrary matrix It is noted in this paper that based on the induction principle such a matrix can be constructed numerically by...
متن کاملTraces of Singular Values and Borcherds Products
Abstract. Let p be a prime for which the congruence group Γ0(p) ∗ is of genus zero, and j∗ p be the corresponding Hauptmodul. Let f be a nearly holomorphic modular form of weight 1/2 on Γ0(4p) which satisfies some congruence condition on its Fourier coefficients. We interpret f as a vector valued modular form. Applying Borcherds lifting of vector valued modular forms we construct infinite produ...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 1991
ISSN: 0989-5558
DOI: 10.5802/jtnb.54