Search results for "kernel"
showing 10 items of 357 documents
Dirichlet Forms, Poincaré Inequalities, and the Sobolev Spaces of Korevaar and Schoen
2004
We answer a question of Jost on the validity of Poincare inequalities for metric space-valued functions in a Dirichlet domain. We also investigate the relationship between Dirichlet domains and the Sobolev-type spaces introduced by Korevaar and Schoen.
An integral representation for decomposable measures of measurable functions
1994
We start with a measurem on a measurable space (Ω,A), decomposable with respect to an Archimedeant-conorm ⊥ on a real interval [0,M], which generalizes an additive measure. Using the integral introduced by the second author, a Radon-Nikodym type theorem, needed in what follows, is given.
On generalized a-Browder's theorem
2007
We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H0(�I T) asbelongs to certain sets of C. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators. 1. Preliminaries. Let L(X) denote the space of bounded linear oper- ators on an infinite-dimensional complex Banach space X. For T ∈ L(X), denote by α(T) the dimension of the kernel ker T, and by β(T) the codi- mension of the range T(X). The operator T ∈ L(X) is called upper semi- Fredholm if α(T) < ∞ and T(X) is closed, and lower …
A space of projections on the Bergman space
2010
We define a set of projections on the Bergman space A 2 , which is parameterized by an ane subset of a Banach space of holomorphic functions in the disk and which includes the classical Forelli-Rudin projections.
On the structure of positive homomorphisms on algebras of real-valued continuous functions
2004
In this paper we study the structure of positive homomorphisms on real function algebras. We prove that every positive homomorphism is completely characterized by a family of sets and when the algebra is inverse-closed, by an ultrafilter of zero-sets of functions of the algebra. We show that the known sufficient conditions for every homomorphism of a real function algebra to be countably evaluating or a point evaluation are not necessary. Our results enable us to characterize the countably evaluating algebras as well as the Lindelof spaces as the spaces in which for every algebra, each countably evaluating homomorphism is a point evaluation.
Classes of operators satisfying a-Weyl's theorem
2005
In this article Weyl's theorem and a-Weyl's theorem on Banach spaces are related to an important property which has a leading role in local spectral theory: the single-valued extension theory. We show that if T has SVEP then Weyl's theorem and a-Weyl's theorem for T are equivalent, and analogously, if T has SVEP then Weyl's theorem and a-Weyl's theorem for T are equivalent. From this result we deduce that a-Weyl's theorem holds for classes of operators for which the quasi-nilpotent part H0(I T ) is equal to ker (I T ) p for some p2N and every 2C, and for algebraically paranormal operators on Hilbert spaces. We also improve recent results established by Curto and Han, Han and Lee, and Oudghi…
Distributed Learning Automata-based S-learning scheme for classification
2019
This paper proposes a novel classifier based on the theory of Learning Automata (LA), reckoned to as PolyLA. The essence of our scheme is to search for a separator in the feature space by imposing an LA-based random walk in a grid system. To each node in the grid, we attach an LA whose actions are the choices of the edges forming a separator. The walk is self-enclosing, and a new random walk is started whenever the walker returns to the starting node forming a closed classification path yielding a many-edged polygon. In our approach, the different LA attached to the different nodes search for a polygon that best encircles and separates each class. Based on the obtained polygons, we perform …
A Survey on Gaussian Processes for Earth-Observation Data Analysis: A Comprehensive Investigation
2016
Gaussian processes (GPs) have experienced tremendous success in biogeophysical parameter retrieval in the last few years. GPs constitute a solid Bayesian framework to consistently formulate many function approximation problems. This article reviews the main theoretical GP developments in the field, considering new algorithms that respect signal and noise characteristics, extract knowledge via automatic relevance kernels to yield feature rankings automatically, and allow applicability of associated uncertainty intervals to transport GP models in space and time that can be used to uncover causal relations between variables and can encode physically meaningful prior knowledge via radiative tra…
Nonlinear PCA for Spatio-Temporal Analysis of Earth Observation Data
2020
Remote sensing observations, products, and simulations are fundamental sources of information to monitor our planet and its climate variability. Uncovering the main modes of spatial and temporal variability in Earth data is essential to analyze and understand the underlying physical dynamics and processes driving the Earth System. Dimensionality reduction methods can work with spatio-temporal data sets and decompose the information efficiently. Principal component analysis (PCA), also known as empirical orthogonal functions (EOFs) in geophysics, has been traditionally used to analyze climatic data. However, when nonlinear feature relations are present, PCA/EOF fails. In this article, we pro…
Advances in Kernel Machines for Image Classification and Biophysical Parameter Retrieval
2017
Remote sensing data analysis is knowing an unprecedented upswing fostered by the activities of the public and private sectors of geospatial and environmental data analysis. Modern imaging sensors offer the necessary spatial and spectral information to tackle a wide range problems through Earth Observation, such as land cover and use updating, urban dynamics, or vegetation and crop monitoring. In the upcoming years even richer information will be available: more sophisticated hyperspectral sensors with high spectral resolution, multispectral sensors with sub-metric spatial detail or drones that can be deployed in very short time lapses. Besides such opportunities, these new and wealthy infor…