Suchergebnisse
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Vor einem Tag · Due to the Weierstrass factorization theorem, analytic functions can be written as infinite products, and these can sometimes be represented as finite products or quotients of the gamma function. We have already seen one striking example: the reflection formula essentially represents the sine function as the product of two gamma functions. Starting from this formula, the exponential function ...
Vor 4 Tagen · This approach was generalized by Karl Weierstrass to what is now known as the Lindemann–Weierstrass theorem. That π is transcendental implies that geometric constructions involving compass and straightedge cannot produce certain results, for example squaring the circle.
Vor 3 Tagen · Section 3 introduces a novel shrinkage operator as a proximity operator of a non-convex function and discusses its properties. In Section 4, we apply the shrinkage operator to solve the tensor completion problem and introduce an effective algorithm for this purpose. We also provide a thorough analysis of the algorithm's convergence and evaluate ...
Vor 4 Tagen · A consequence of Casorati-Weierstrass is that, if there are constants $R_0, C, s$ such that $f(\mathbb{C}\setminus K_R(0)) \subset \mathbb{C} \setminus K_{CR^s}(0)$ for all $R>R_0$, then $f$ must be a polynomial. Is the inverse true as well? Does this hold for any complex polynomial?
Vor 5 Tagen · The density of their span is a consequence of the Stone–Weierstrass theorem, but follows also from the properties of classical kernels like the Fejér kernel. Fourier theorem proving convergence of Fourier series
Vor 3 Tagen · The Stone-Weierstrass theorem asserts that any continuous function on an interval can be approximated by polynomials. This means that, in theory, polynomial logistic regression can approximate any continuous decision boundary. However, in practice, the choice of polynomial degree is crucial to avoid overfitting or underfitting.
Vor einem Tag · In the paper, we consider both finite-dimensional and infinite-dimensional optimization problems with inclusion-type and equality-type constraints. We obtain sufficient conditions for the stability in the weak topology of a solution to this problem with respect to small perturbations of the problem parameters. In the finite-dimensional case, conditions for the stability in the strong topology ...
