Spectral measures and automatic continuity

Spectral measures and automatic continuity

Let X be a locally convex Hausdorff space (briefly, lcHs) and L(X) denote the space of all continuous linear operators of X into itself. The space L(X) is denoted by Ls(X) when it is equipped with the topology of pointwise convergence in X (i.e. the strong operator topology). By a spectral measure in X is meant a σ-additive map P : Σ → Ls(X), defined on a σ-algebra Σ of subsets of some set Ω, w...

Spectral Continuity Measures at Mandarin Syllable Boundaries

In Text-to-Speech (TTS) systems based on concatenative synthesis, the naturalness of synthetic speech is highly affected by the spectral continuities at the concatenation point. In this paper, we focused on 4 kinds of syllable boundaries in mandarin and used several spectral distance measures combined with time derivatives distance measures to predict their audible discontinuities. A perceptual...

Banach module valued separating maps and automatic continuity

For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...

Feature extraction for spectral continuity measures in concatenative speech synthesis

The quality of concatenative speech synthesis depends on the cost function employed for unit selection. Effective cost functions for spectral continuity are difficult to define and standard measures often do not accurately reflect human perception of discontinuity across a concatenated join. In this study the performance of a number of standard distance measures are compared for the task of det...

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras