In this paper, Part II of a series of eight papers on logarithmic tensor category theory, we develop logarithmic formal calculus and study logarithmic intertwining operators.
Logarithmic tensor category theory, II: Logarithmic formal calculus and properties of logarithmic intertwining operators
In this “logarithmic formal calculus,” we establish certain properties, some of them quite subtle, of the formal derivative operator d/dx acting on such spaces.
Logarithmic tensor category theory, II: Logarithmic formal calculus and properties of logarithmic intertwining operators
The functional calculus can be extended to unbounded operators, and it is a theorem that N Γ satisﬁes the Ore condition, with S as the set of all non-zero divisors, and that this Ore localisation yields U Γ.
A Second Order Algebraic Knot Concordance Group
B dependent part is interpreted in the sense of operator calculus for selfadjoint operators.
Dispersive estimates for principally normal pseudodifferential operators
L∞ . λ−1kcαkC 2 We also introduce the modiﬁed operators, ˜Pφ,λ = X|α|=m cα,λ (x/µ)(D , µ)α somewhat in the spirit of the paradifferential calculus.
Dispersive estimates for principally normal pseudodifferential operators
Stochastic calculus of variations and hypoelliptic operators.
Hypoellipticity in infinite dimensions and an application in interest rate theory
Zarikian, The calculus of one-sided M -ideals and multipliers in operator spaces, Mem.
Open partial isometries and positivity in operator spaces
Given the distributed and concurrent nature of sensor network operations, we build our sensor network model based on process calculi [7, 13] and also on an ob ject calculus to introduce state into the sensors.
A Formal Model for Programming Wireless Sensor Networks
Now we deﬁne basic operators associated with toy Fock space Γ(Sh ) using the fundamental processes in coordinate-free language of quantum stochastic calculus, developed in .
Quantum random walks and vanishing of the second Hochschild cohomology
The proof of [HaWu] is based on the construction of a global parametrix for the kernel of the Schr¨odinger propagator e−itH , and requires a considerable amount of microlocal machinery (such as the scattering calculus of pseudodifferential operators, introduced by R.B.
Analytic wave front set for solutions to Schroedinger equation
Then, different choices for C give equivalent elements in H0,(z0 ,ζ0 ) , and the substitution of σA to a in (A.3) gives rise to the same operator up to an exponentially small error term in the norm k · kΦ,Ω0 ,Ω1 . σA is called the symbol of A, and the usual symbolic calculus extends to such operators.
Analytic wave front set for solutions to Schroedinger equation
In models based on channeled communications (as in the π-calculus ), we can partition the threads according to the name of the channel they operate on.
Partitioning the Threads of a Mobile System
Synthesis of logic networks whose operators are described by means of singleplace predicate calculus.
Efficient Algorithms for Membership in Boolean Hierarchies of Regular Languages
Borel functional calculus of the operator T .
Integral equalities for functions of unbounded spectral operators in Banach spaces
To prove Theorem 1.4 we will employ a parameter-dependent parametrix of A − λ in the calculus of cusp pseudodifferential operators on M to approximate the resolvent.
Maximal regularity for parabolic partial differential equations on manifolds with cylindrical ends
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