We prove that the class of context-free languages with polynomially bounded ambiguity (PCFL) is the closure of the class of unambiguous languages (UCFL) under projections which deletes Parikh bounded symbols only. A symbol a is Parikh bounded in a language L if there is a constant c such that no word of L contains more than c occurrences of a. Furthermore PCFL is closed under the formally stron...

This paper deals with the problem∆u= g onG and ∂u/∂n+u f = L on ∂G. Here,G⊂ Rm, m> 2, is a bounded domain with Lyapunov boundary, f is a bounded nonnegative function on the boundary of G, L is a bounded linear functional onW1,2(G) representable by a real measure μ on the boundary of G, and g ∈ L2(G)∩Lp(G), p > m/2. It is shown that a weak solution of this problem is bounded in G if and only if ...

The degree qj’a graph H is the maximum among the degrees of its nodes. A set of graphs L is of bounded degree if there exists a positive integer n such that the degree of each graph in L does not exceed n. We demonstrate that it is decidable whether or not the (graph) language of an arbitrary node label controlled (NLC) grammar is of bounded degree. Moreover, it is shown that, given an arbitrar...

A bounded linear operator that maps H to L and L to L is bounded from L to L for each p ∈ (1, 2), by a famous interpolation result of Fefferman and Stein. We prove L-norm bounds that grow like O ( 1/(p− 1) ) as p ↓ 1. This growth rate is optimal, and improves significantly on the previously known exponential bound O(21/(p−1)).

Given integers i, j, k, L,M , we establish a new double bounded q−series identity from which the three parameter (i, j, k) key identity of Alladi-Andrews-Gordon for Göllnitz’s (big) theorem follows if L,M → ∞. When L = M , the identity yields a strong refinement of Göllnitz’s theorem with a bound on the parts given by L. This is the first time a bounded version of Göllnitz’s (big) theorem has b...

Let $N$ be a closed manifold and $U \subset T^\*(N)$ bounded domain in the cotangent bundle of $N$, containing zero-section. A conjecture due to Viterbo asserts that spectral metric for Lagrangian submanifolds $U$ are exact-isotopic zero-section is bounded. In this paper we establish an upper bound on distance between two such Lagrangians $L\_0, L\_1$, which depends linearly boundary depth Floe...

We completely characterize the boundedness on Wiener amalgam spaces of the short-time Fourier transform (STFT), and on both L and Wiener amalgam spaces of a special class of pseudodifferential operators, called localization operators. Precisely, sufficient conditions for the STFT to be bounded on the Wiener amalgam spaces W (L, L) are given and their sharpness is shown. Localization operators a...

For a polynomial P (ξ) in ξ in R with constant complex coefficients, the operator defined by R(z)f = F((P (·)−z)f̂), where ∧ denotes the Fourier transform and F denotes its inverse, is not bounded from L to L when z is in the spectrum of P (D). What are suitable spaces B and C so that R(z) is bounded from B to C? When P (ξ) is simply characteristic, we prove that the operator R(z) is bounded fro...