Subject List مقالات لاتين ديجيتال We generalize our recent results on the boundedness and compactness of Toeplitz operators to the Bergman space A1 on the unit disc. While the natural condition for the symbols leads to BMO¶-type symbol classes, the inevitable logarithmic correction for the nonreflexive case requires a separate treatment of BA-and BO-type symbols. We use the boundary-path space of a finitely-aligned k-graphLto construct a compactly-aligned product system X, and we show that the graph algebra C_(L) is isomorphic to the Cuntz–Nica–Pimsner algebra NO(X). In this setting, we introduce the notion of a crossed product by a semigroup of partial endomorphisms and partially-defined transfer operators by defining it

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1

We generalize our recent results on the boundedness and compactness of Toeplitz operators to the Bergman space A1 on the unit disc. While the natural condition for the symbols leads to BMO¶-type symbol classes, the inevitable logarithmic correction for the nonreflexive case requires a separate treatment of BA-and BO-type symbols.

2

We obtain Gaussian upper bounds for heat kernels of higher order differential operators with Dirichlet boundary conditions on bounded domains in RN. The bounds exhibit explicitly the nature of the spatial decay of the heat kernel close to the boundary as well as the long-time exponential decay implied by the spectral gap. We make no smoothness assumptions on our operator coefficients which we assume only to be bounded and measurable

3

We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in noncommuting variables with values invariant under cyclic permutations of the indexes, is called a tracial sequence. We prove that such a sequence can be represented with tracial moments of matrices if its corresponding moment matrix is positive semidefinite and of finite rank. A truncated tracial sequence allows for such a representation if and only if one of its extensions admits a flat extension. Finally, we apply this theory via duality to investigate tracepositive polynomials in noncommuting variables.

4

We use the boundary-path space of a finitely-aligned k-graphLto construct a compactly-aligned product system X, and we show that the graph algebra C_(L) is isomorphic to the Cuntz–Nica–Pimsner algebra NO(X). In this setting, we introduce the notion of a crossed product by a semigroup of partial endomorphisms and partially-defined transfer operators by defining it