A Random Evolution Inclusion of Subdifferential Type in Hilbert Spaces

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6].

Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities

Mathematics Subject Classification: 47A56, 47A57,47A63

Hilbert-Smith Conjecture for K - Quasiconformal Groups

MSC 2010: 30C60

A Smooth Four-Dimensional G-Hilbert Scheme

2000 Mathematics Subject Classification: 14C05, 14L30, 14E15, 14J35.

Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)

2000 Mathematics Subject Classification: Primary 14E15; Secondary 14C05,14L30.

Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces

2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.

Riemann-Hilbert Problems with Canonical Normalization and Families of Commuting Operators

2010 Mathematics Subject Classification: 35Q15, 31A25, 37K10, 35Q58.

Multipliers on Spaces of Functions on a Locally Compact Abelian Group with Values in a Hilbert Space

2000 Mathematics Subject Classification: Primary 43A22, 43A25.

Multipliers on a Hilbert Space of Functions on R

2000 Mathematics Subject Classification: 42A45.

Operatori lineari su spazi di Hilbert

La trattazione che segue fornisce un'introduzione agli operatori lineari. Il primo capitolo contiene dei cenni sugli spazi di Hilbert di dimensione infinita, in modo da poter lavorare con operatori definiti non solo su spazi finito dimensionali, che sono generalmente rappresentati da matrici. Nel secondo capitolo si prosegue con lo studio degli operatori lineari limitati, proponendo come esempio l'operatore di proiezione. Viene definito anche l'importante concetto di operatore aggiunto, generalizzato nel capitolo successivo. Il capitolo finale tratta gli operatori non limitati, che possono essere analizzati con più facilità se soddisfano una proprietà topologica, che è la chiusura. Si affronta anche il concetto di spettro di un operatore, soprattutto nel caso di un operatore autoaggiunto, concludendo con l' esempio di un importante operatore, cioè l'operatore differenziale, fondamentale in meccanica quantistica.

Rota’s universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In articular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Irreducibility of Random Hilbert Schemes

We prove that a random Hilbert scheme that parametrizes the closed subschemes with a fixed Hilbert polynomial in some projective space is irreducible and nonsingular with probability greater than $0.5$. To consider the set of nonempty Hilbert schemes as a probability space, we transform this set into a disjoint union of infinite binary trees, reinterpreting Macaulay's classification of admissible Hilbert polynomials. Choosing discrete probability distributions with infinite support on the trees establishes our notion of random Hilbert schemes. To bound the probability that random Hilbert schemes are irreducible and nonsingular, we show that at least half of the vertices in the binary trees correspond to Hilbert schemes with unique Borel-fixed points.

Riemann-Hilbert problems for poly-Hardy space on the unit ball

In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly- Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane.

A simple but efficient voice activity detection algorithm through Hilbert transform and dynamic threshold for speech pathologies

A simple but efficient voice activity detector based on the Hilbert transform and a dynamic threshold is presented to be used on the pre-processing of audio signals -- The algorithm to define the dynamic threshold is a modification of a convex combination found in literature -- This scheme allows the detection of prosodic and silence segments on a speech in presence of non-ideal conditions like a spectral overlapped noise -- The present work shows preliminary results over a database built with some political speech -- The tests were performed adding artificial noise to natural noises over the audio signals, and some algorithms are compared -- Results will be extrapolated to the field of adaptive filtering on monophonic signals and the analysis of speech pathologies on futures works

Aplicación de los anillos noetherianos conmutativos y las variedades algebraicas afines en la demostración del teorema de los ceros de Hilbert

Se desarrolla un estudio de todas las herramientas necesarias para llegar al teorema de los ceros de Hilbert el cual luego se demuestra en sus formas débil y fuerte. Se introducen los conceptos básicos relacionados con los anillos noetherianos y las variedades algebraicas afines que son fundamentales para el estudio del teorema de los ceros de Hilbert. Es por ello que estudiamos detenidamente el concepto de ideal primo e ideal primario, como también las distintas operaciones entre ideales, en particular la descomposición primaria de ideales. En seguida se desarrollan las demostraciones de algunos de los teoremas importantes de los anillos noetherianos, haciendo uso de la descomposición primaria de un ideal y un resultado fundamental: el teorema de la base de Hilbert. Además se desarrollan las definiciones, proposiciones, teoremas de una variedad algebraica afín y el ideal asociado a una variedad, así como también el ideal de una variedad y lo más interesante es la descomposición de ideales en variedades algebraicas afines, como la condición de cadena descendente de variedades. También se hace la aplicación de los resultados obtenidos en los capítulos anteriores, para demostrar el teorema de los ceros de Hilbert en su forma dedil así como en la forma fuerte. Finalmente adoptamos una Topología que es muy débil pero sorprendentemente útil ocupando los resultados anteriores, probando propiedades que cumple esta topología como la cerradura topológica y compacidad.