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Competition of Species with Intra-Specific Competition

N. Apreutesei, A. Ducrot, V. Volpert (2008)

Mathematical Modelling of Natural Phenomena

Intra-specific competition in population dynamics can be described by integro-differential equations where the integral term corresponds to nonlocal consumption of resources by individuals of the same population. Already the single integro-differential equation can show the emergence of nonhomogeneous in space stationary structures and can be used to model the process of speciation, in particular, the emergence of biological species during evolution [S. Genieys et al., Math. Model. Nat. Phenom....

Complementary triangular forms

Rob Zuidwijk (1997)

Banach Center Publications

The notion of simultaneous reduction of pairs of matrices and linear operators to triangular forms is introduced and a survey of known material on the subject is given. Further, some open problems are pointed out throughout the text. The paper is meant to be accessible to the non-specialist and does not contain any new results or proofs.

Complete Pick positivity and unitary invariance

Angshuman Bhattacharya, Tirthankar Bhattacharyya (2010)

Studia Mathematica

The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foiaş. Just as a contraction is related to the Szegö kernel k S ( z , w ) = ( 1 - z w ̅ ) - 1 for |z|,|w| < 1, by means of ( 1 / k S ) ( T , T * ) ≥ 0 , we consider an arbitrary open connected domain Ω in ℂⁿ, a complete Pick kernel k on Ω and a tuple T = (T₁, ..., Tₙ) of commuting bounded operators on a complex separable Hilbert space ℋ such that (1/k)(T,T*) ≥ 0. For a complete Pick kernel the 1/k functional calculus makes sense in a beautiful...

Completely monotone functions of finite order and Agler's conditions

Sameer Chavan, V. M. Sholapurkar (2015)

Studia Mathematica

Motivated by some structural properties of Drury-Arveson d-shift, we investigate a class of functions consisting of polynomials and completely monotone functions defined on the semi-group ℕ of non-negative integers, and its operator-theoretic counterpart which we refer to as the class of completely hypercontractive tuples of finite order. We obtain a Lévy-Khinchin type integral representation for the spherical generating tuples associated with such operator tuples and discuss its applications.

Complétude des noyaux reproduisants dans les espaces modèles

Emmanuel Fricain (2002)

Annales de l’institut Fourier

Soit ( λ n ) n ≥ 1 une suite de Blaschke du disque unité 𝔻 et Θ une fonction intérieure. On suppose que la suite de noyaux reproduisants k Θ ( z , λ n ) : = 1 - Θ ( λ n ) ¯ Θ ( z ) 1 - λ n ¯ z n ≥ 1 est complète dans l’espace modèle K Θ p : = H p ∩ Θ H 0 p ¯ , 1 &lt; p &lt; + ∞ . On étudie, dans un premier temps, la stabilité de cette propriété de complétude, à la fois sous l’effet de perturbations des fréquences ( λ n ) n ≥ 1 mais également sous l’effet de perturbations de la fonction Θ . On retrouve ainsi un certain nombre de résultats classiques sur les systèmes d’exponentielles. Puis, si on suppose de plus que la suite ...

Composition operators and the Hilbert matrix

E. Diamantopoulos, Aristomenis Siskakis (2000)

Studia Mathematica

The Hilbert matrix acts on Hardy spaces by multiplication with Taylor coefficients. We find an upper bound for the norm of the induced operator.

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