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pro vyhledávání: '"Talvila, Erik"'
Autor:
Talvila, Erik
For each $1\leq p<\infty$ a Banach space of integrable Schwartz distributions is defined by taking the distributional derivative of all functions in $L^p({\mathbb R})$. Such distributions can be integrated when multiplied by a function that is the in
Externí odkaz:
http://arxiv.org/abs/2309.07821
Autor:
Talvila, Erik
For each $f\in L^p({\mathbb R)}$ ($1\leq p<\infty$) it is shown that the Fourier transform is the distributional derivative of a H\"older continuous function. For each $p$ a norm is defined so that the space Fourier transforms is isometrically isomor
Externí odkaz:
http://arxiv.org/abs/2309.01699
Autor:
Talvila, Erik
Sharp estimates of solutions of the classical heat equation are proved in $L^p$ norms on the real line.
Externí odkaz:
http://arxiv.org/abs/2301.00769
Autor:
Talvila, Erik
In this paper we prove pointwise and distributional Fourier transform inversion theorems for functions on the real line that are locally of bounded variation, while in a neighbourhood of infinity are Lebesgue integrable or have polynomial growth. We
Externí odkaz:
http://arxiv.org/abs/2203.13942
Autor:
Talvila, Erik
If $f\in L^1({\mathbb R})$ it is proved that $\lim_{S\to\infty}\lVert f-f\ast D_S\rVert=0$, where $D_S(x)=\sin(Sx)/(\pi x)$ is the Dirichlet kernel and $\lVert f\rVert = \sup_{\alpha<\beta}|\int_{\alpha}^{\beta}f(x)\,dx|$ is the Alexiewicz norm. This
Externí odkaz:
http://arxiv.org/abs/2202.01359
Autor:
Talvila, Erik
Three methods of least squares are examined for fitting a line to points in the plane. Two well known methods are to minimize sums of squares of vertical or horizontal distances to the line. Less known is to minimize sums of squares of distances to t
Externí odkaz:
http://arxiv.org/abs/2011.04836
Autor:
Talvila, Erik
An integral is defined on the plane that includes the Henstock--Kurzweil and Lebesgue integrals (with respect to Lebesgue measure). A space of primitives is taken as the set of continuous real-valued functions $F(x,y)$ defined on the extended real pl
Externí odkaz:
http://arxiv.org/abs/1906.11789
Autor:
Grant, Cameron, Talvila, Erik
Approximations to the integral $\int_a^b\int_c^d f(x,y)\,dy\,dx$ are obtained under the assumption that the partial derivatives of the integrand are in an $L^p$ space, for some $1\leq p\leq\infty$. We assume ${\lVert f_{xy}\rVert}_p$ is bounded (inte
Externí odkaz:
http://arxiv.org/abs/1905.05805
Autor:
Talvila, Erik
Let $f$ be a function on the real line. The Fourier transform inversion theorem is proved under the assumption that $f$ is absolutely continuous such that $f$ and $f'$ are Lebesgue integrable. A function $g$ is defined by $f'(t)-iwf(t)=g(t)$. This di
Externí odkaz:
http://arxiv.org/abs/1808.04313
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