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Normal approximations for wavelet coefficients on spherical Poisson fields ; ; Peccati, Giovanni in Journal of Mathematical Analysis & Applications (2014), 409(1), 212--227 Detailed reference viewed: 131 (5 UL)Measuring the interactions among variables of functions over the unit hypercube Marichal, Jean-Luc ; Mathonet, Pierre in Journal of Mathematical Analysis & Applications (2011), 380(1), 105-116 By considering a least squares approximation of a given square integrable function $f\colon[0,1]^n\to\R$ by a multilinear polynomial of a specified degree, we define an index which measures the overall ... [more ▼] By considering a least squares approximation of a given square integrable function $f\colon[0,1]^n\to\R$ by a multilinear polynomial of a specified degree, we define an index which measures the overall interaction among variables of $f$. This definition extends the concept of Banzhaf interaction index introduced in cooperative game theory. Our approach is partly inspired from multilinear regression analysis, where interactions among the independent variables are taken into consideration. We show that this interaction index has appealing properties which naturally generalize the properties of the Banzhaf interaction index. In particular, we interpret this index as an expected value of the difference quotients of $f$ or, under certain natural conditions on $f$, as an expected value of the derivatives of $f$. These interpretations show a strong analogy between the introduced interaction index and the overall importance index defined by Grabisch and Labreuche [7]. Finally, we discuss a few applications of the interaction index. [less ▲] Detailed reference viewed: 81 (3 UL)Universality properties of Taylor series inside the domain of holomorphy ; Meyrath, Thierry ; in Journal of Mathematical Analysis & Applications (2011), 383(1), 234-238 It is proven that the Taylor series of functions holomorphic in $\C_{\infty} \setminus \{1\}$ generically have certain universality properties on small sets outside the unit disk. Moreover, it is shown ... [more ▼] It is proven that the Taylor series of functions holomorphic in $\C_{\infty} \setminus \{1\}$ generically have certain universality properties on small sets outside the unit disk. Moreover, it is shown that such sets necessarily are polar sets. [less ▲] Detailed reference viewed: 114 (4 UL)Evolution semigroups and time operators on Banach spaces Suchanecki, Zdzislaw ; in Journal of Mathematical Analysis & Applications (2010), 371(2), 454-464 We present new general methods to obtain shift representation of evolution semigroups defined on Banach spaces. We introduce the notion of time operator associated with a generalized shift on a Banach ... [more ▼] We present new general methods to obtain shift representation of evolution semigroups defined on Banach spaces. We introduce the notion of time operator associated with a generalized shift on a Banach space and give some conditions under which time operators can be defined on an arbitrary Banach space. We also tackle the problem of scaling of time operators and obtain a general result about the existence of time operators on Banach spaces satisfying some geometric conditions. The last part of the paper contains some examples of explicit constructions of time operators on function spaces. [less ▲] Detailed reference viewed: 56 (0 UL)An example of a weighted algebra $L_p^w(G)$ on uncountable group Kuznetsova, Julia in Journal of Mathematical Analysis & Applications (2009), 353(2), 660-665 Detailed reference viewed: 13 (1 UL)Multivariate integration of functions depending explicitly on the minimum and the maximum of the variables Marichal, Jean-Luc in Journal of Mathematical Analysis & Applications (2008), 341(1), 200-210 By using some basic calculus of multiple integration, we provide an alternative expression of the integral $$ \int_{]a,b[^n} f(\mathbf{x},\min x_i,\max x_i) \, d\mathbf{x}, $$ in which the minimum and the ... [more ▼] By using some basic calculus of multiple integration, we provide an alternative expression of the integral $$ \int_{]a,b[^n} f(\mathbf{x},\min x_i,\max x_i) \, d\mathbf{x}, $$ in which the minimum and the maximum are replaced with two single variables. We demonstrate the usefulness of that expression in the computation of orness and andness average values of certain aggregation functions. By generalizing our result to Riemann-Stieltjes integrals, we also provide a method for the calculation of certain expected values and distribution functions. [less ▲] Detailed reference viewed: 84 (4 UL)Uniformity and inexact version of a proximal method for metrically regular mappings Aragón Artacho, Francisco Javier ; in Journal of Mathematical Analysis & Applications (2007), 335(1), 168-183 We study stability properties of a proximal point algorithm for solving the inclusion 0∈T(x) when T is a set-valued mapping that is not necessarily monotone. More precisely we show that the convergence of ... [more ▼] We study stability properties of a proximal point algorithm for solving the inclusion 0∈T(x) when T is a set-valued mapping that is not necessarily monotone. More precisely we show that the convergence of our algorithm is uniform, in the sense that it is stable under small perturbations whenever the set-valued mapping T is metrically regular at a given solution. We present also an inexact proximal point method for strongly metrically subregular mappings and show that it is super-linearly convergent to a solution to the inclusion 0∈T(x). [less ▲] Detailed reference viewed: 65 (4 UL) |
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