The Experts below are selected from a list of 99 Experts worldwide ranked by ideXlab platform
Sandra Saliani - One of the best experts on this subject based on the ideXlab platform.
-
$\ell ^2$-Linear independence for the system of integer translates of a Square Integrable Function
Proceedings of the American Mathematical Society, 2012Co-Authors: Sandra SalianiAbstract:We prove that if the system of integer translates of a Square Integrable Function is l^2-linear independent then its periodization Function is strictly positivealmost everywhere. Indeed we show that the above inference holds for any Square Integrable Function since the following statement on Fourier analysis is true: For any (Lebesgue) measurable subset A of [0, 1], with positive measure,\ud there exists a non trivial Square summable Function, with support in A, whose partial sums of Fourier series are uniformly bounded in the uniform norm. This answers a question posed by Guido Weiss
-
ell 2 linear independence for the system of integer translates of a Square Integrable Function
arXiv: Classical Analysis and ODEs, 2010Co-Authors: Sandra SalianiAbstract:We prove that if the system of integer translates of a Square Integrable Function is $\ell^2$-linear independent then its periodization Function is strictly positive almost everywhere. Indeed we show that the above inference is true for any Square Integrable Function since the following statement on Fourier analysis is true: For any (Lebesgue) measurable subset A of [0,1], with positive measure, there exists a non trivial Square summable Function, with support in A, whose partial sums of Fourier series are uniformly bounded.
-
$\ell^2$-Linear Independence for the System of Integer Translates of a Square Integrable Function
arXiv: Classical Analysis and ODEs, 2010Co-Authors: Sandra SalianiAbstract:We prove that if the system of integer translates of a Square Integrable Function is $\ell^2$-linear independent then its periodization Function is strictly positive almost everywhere. Indeed we show that the above inference is true for any Square Integrable Function since the following statement on Fourier analysis is true: For any (Lebesgue) measurable subset A of [0,1], with positive measure, there exists a non trivial Square summable Function, with support in A, whose partial sums of Fourier series are uniformly bounded.
Valery Serov - One of the best experts on this subject based on the ideXlab platform.
-
the fourier series of a Square Integrable Function the riesz fischer theorem
2017Co-Authors: Valery SerovAbstract:The set of Square-Integrable Functions \(L^2(-\pi ,\pi )\) is an inner product space (linear Euclidean space) equipped with the inner product
-
The Fourier Series of a Square-Integrable Function. The Riesz–Fischer Theorem.
Applied Mathematical Sciences, 2017Co-Authors: Valery SerovAbstract:The set of Square-Integrable Functions \(L^2(-\pi ,\pi )\) is an inner product space (linear Euclidean space) equipped with the inner product
Santosh S. Venkatesh - One of the best experts on this subject based on the ideXlab platform.
-
On approximations of Functions by depth-two neural networks
Proceedings of 1994 IEEE International Symposium on Information Theory, 1994Co-Authors: Santosh S. VenkateshAbstract:The simple Pythagorean notion of orthogonal projections is used to show that depth-two sigmoidal neural networks can approximate any Square-Integrable Function with compact support in R/sup n/ with arbitrarily small integrated Squared-error. >
Saswata Adhikari - One of the best experts on this subject based on the ideXlab platform.
-
left translates of a Square Integrable Function on the heisenberg group
Collectanea Mathematica, 2019Co-Authors: R Radha, Saswata AdhikariAbstract:The aim of this paper is to study some properties of left translates of a Square Integrable Function on the Heisenberg group. First, a necessary and sufficient condition for the existence of the canonical dual to a Function $$\varphi \in L^{2}(\mathbb {R}^{2n})$$ is obtained in the case of twisted shift-invariant spaces. Further, characterizations of $$\ell ^{2}$$ -linear independence and the Hilbertian property of the twisted translates of a Function $$\varphi \in L^{2}(\mathbb {R}^{2n})$$ are obtained. Later these results are shown in the case of the Heisenberg group.
R Radha - One of the best experts on this subject based on the ideXlab platform.
-
left translates of a Square Integrable Function on the heisenberg group
Collectanea Mathematica, 2019Co-Authors: R Radha, Saswata AdhikariAbstract:The aim of this paper is to study some properties of left translates of a Square Integrable Function on the Heisenberg group. First, a necessary and sufficient condition for the existence of the canonical dual to a Function $$\varphi \in L^{2}(\mathbb {R}^{2n})$$ is obtained in the case of twisted shift-invariant spaces. Further, characterizations of $$\ell ^{2}$$ -linear independence and the Hilbertian property of the twisted translates of a Function $$\varphi \in L^{2}(\mathbb {R}^{2n})$$ are obtained. Later these results are shown in the case of the Heisenberg group.