Search results for " function"
showing 10 items of 9395 documents
New spaces of matrices with operator entries
2019
In this paper, we will consider matrices with entries in the space of operators $\mathcal{B}(H)$, where $H$ is a separable Hilbert space and consider the class of matrices that can be approached in the operator norm by matrices with a finite number of diagonals. We will use the Schur product with Toeplitz matrices generated by summability kernels to describe such a class and show that in the case of Toeplitz matrices it can be identified with the space of continuous functions with values in $\mathcal B(H)$. We shall also introduce matriceal versions with operator entries of classical spaces of holomorphic functions such as $H^\infty(\mathbb{D})$ and $A(\mathbb{D})$ when dealing with upper t…
A Unifying Approach to Weyl Type Theorems for Banach Space Operators
2013
Weyl type theorems have been proved for a considerably large number of classes of operators. In this paper, by introducing the class of quasi totally hereditarily normaloid operators, we obtain a theoretical and general framework from which Weyl type theorems may be promptly established for many of these classes of operators. This framework also entails Weyl type theorems for perturbations f(T + K), where K is algebraic and commutes with T, and f is an analytic function, defined on an open neighborhood of the spectrum of T + K, such that f is non constant on each of the components of its domain.
Generalized Schröder permutations
2013
We give the generating function for the integer sequence enumerating a class of pattern avoiding permutations depending on two parameters: m and p. The avoided patterns are the permutations of length m with the largest element in the first position and the second largest in one of the last p positions. For particular instances of m and p we obtain pattern avoiding classes enumerated by Schroder, Catalan and central binomial coefficient numbers, and thus, the obtained two-parameter generating function gathers under one roof known generating functions and expresses new ones. This work generalizes some earlier results of Barcucci et al. (2000) [2], Kremer (2000) [5] and Kremer (2003) [6].
Restricted 123-avoiding Baxter permutations and the Padovan numbers
2007
AbstractBaxter studied a particular class of permutations by considering fixed points of the composite of commuting functions. This class is called Baxter permutations. In this paper we investigate the number of 123-avoiding Baxter permutations of length n that also avoid (or contain a prescribed number of occurrences of) another certain pattern of length k. In several interesting cases the generating function depends only on k and is expressed via the generating function for the Padovan numbers.
Combinatorial aspects of L-convex polyominoes
2007
We consider the class of L-convex polyominoes, i.e. those polyominoes in which any two cells can be connected with an ''L'' shaped path in one of its four cyclic orientations. The paper proves bijectively that the number f"n of L-convex polyominoes with perimeter 2(n+2) satisfies the linear recurrence relation f"n"+"2=4f"n"+"1-2f"n, by first establishing a recurrence of the same form for the cardinality of the ''2-compositions'' of a natural number n, a simple generalization of the ordinary compositions of n. Then, such 2-compositions are studied and bijectively related to certain words of a regular language over four letters which is in turn bijectively related to L-convex polyominoes. In …
Enumerable classes of total recursive functions: Complexity of inductive inference
1994
This paper includes some results on complexity of inductive inference for enumerable classes of total recursive functions, where enumeration is considered in more general meaning than usual recursive enumeration. The complexity is measured as the worst-case mindchange (error) number for the first n functions of the given class. Three generalizations are considered.
Analytic Extension of Non Quasi - Analytic Whitney Jets of Beurling Type
1998
Let (Mr)r∈ℕ0 be a logarithmically convex sequence of positive numbers which verifies M0 = 1 as well as Mr ≥ 1 for every r ∈ ℕ and defines a non quasi - analytic class. Let moreover F be a closed proper subset of ℝn. Then for every function f on ℝn belonging to the non quasi - analytic (Mr)-class of Beurling type, there is an element g of the same class which is analytic on ℝ,nF and such that Dαf(x) = Dαg(x) for every α ∈ ℕn0 and x ∈ F.
Mappings of finite distortion: The zero set of the Jacobian
2003
This paper is part of our program to establish the fundamentals of the theory of mappings of finite distortion [6], [1], [8], [13], [14], [7] which form a natural generalization of the class of mappings of bounded distortion, also called quasiregular mappings. Let us begin with the definition. We assume that Ω ⊂ Rn is a connected open set. We say that a mapping f : Ω → Rn has finite distortion if:
Dimensions of random affine code tree fractals
2014
We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.
On positive P
2002
Continuing a line of research opened up by Grigni and Sipser (1992) and further pursued by Stewart (1994), we show that a wide variety of equivalent characterizations of P still remain equivalent when restricted to be positive. All these restrictions thus define the same class posP, a proper subclass of monP, the class of monotone problems in P. We also exhibit complete problems for posP under very weak reductions.