We use the standard notations: differential forms ap, their exterior algebra A, exterior derivative d<p, Hodge's star operator *, coderivative 3f = (_ 1)nP + n 1*d*(P, Laplace-Beltrami operator A = d3 + Md, exterior product (pAg,, inner product (so,*) = fJmpA*4p, and the Dirichlet norm D(sp) = (dep, dp) + (a<p, 5op). For 0forms u the norm reduces to D(u) = (du, du), and Au has the representation

The extension principle defines the arithmetic operations on fuzzy numbers. In the extension principle one can use any t-norm for modeling the conjunction operator. It is therefore important to know, which t-norms are consistent with a particular type of fuzzy number. We call a t-norm consistent, if the arithmetic operation is closed. In this paper we investigate the addition of sigmoid and two...

We define the complete numerical radius norm for homomorphisms from any operator algebra into B(H), and show that this norm can be computed explicitly in terms of the completely bounded norm. This is used to show that if K is a complete Cspectral set for an operator T , then it is a complete M -numerical radius set, where M = 12 (C + C −1). In particular, in view of Crouzeix’s theorem, there is...

We present results concerning resolvent estimates for the linear operator associated with the system of differential equations governing perturbations of the Couette flow. We prove estimates on the norm of the resolvent of this operator showing this norm to be proportional to the Reynolds number R for a region of the complex plane. Numerical approximations indicate that the same dependence is v...

In combination with simultaneous approximation terms, summation-by-parts (SBP) operators provide a flexible and efficient methodology that leads to consistent, conservative, and provably stable high-order discretizations. Traditional diagonal-norm SBP operators with a repeating interior point operator lead to solutions that have a global order of accuracy lower than the order of the interior po...

Abstract. We consider functions f(A,B) of noncommuting self-adjoint operators A and B that can be defined in terms of double operator integrals. We prove that if f belongs to the Besov class B ∞,1 (R), then we have the following Lipschitz type estimate in the trace norm: ‖f(A1, B1)− f(A2, B2)‖S1 ≤ const(‖A1 −A2‖S1 + ‖B1 −B2‖S1). However, the condition f ∈ B ∞,1 (R) does not imply the Lipschitz ...

We use induction and interpolation techniques to prove that a composition operator induced by a map φ is bounded on the weighted Bergman space Aα(H) of the right half-plane if and only if φ fixes ∞ non-tangentially, and has a finite angular derivative λ there. We further prove that in this case the norm, essential norm, and spectral radius of the operator are all equal, and given by λ.

It is well known that for multipliers f of the Drury-Arveson space H n, ‖f‖∞ does not dominate the operator norm of Mf . We show that in general ‖f‖∞ does not even dominate the essential norm of Mf . A consequence of this is that there exist multipliers f of H n for which Mf fails to be essentially hyponormal, i.e., if K is any compact, self-adjoint operator, then the inequality M∗ f Mf −MfM f ...

Lipschitzian and kernel aggregation operators with respect to the natural T indistinguishability operator ET and their powers are studied. A t-norm T is proved to be ET -lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the more stable aggregation operator w...

Let 0 ≤ T : L(Y, ν) → L(X,μ) be a positive linear operator and let ‖T‖p,q denote its operator norm. In this paper a method is given to compute ‖T‖p,q exactly or to bound ‖T‖p,q from above. As an application the exact norm ‖V ‖p,q of the Volterra operator V f(x) = ∫ x 0 f(t)dt is computed. Department of Mathematics, University of South Carolina, Columbia, SC 29208 1991 Mathematics Subject Classi...