Abstract We establish the local-to-global property of synthetic curvature-dimension condition for essentially non-branching locally finite metric-measure spaces, extending work [Cavalletti and Milman in Invent Math 226(1):1–137, 2021].

We present supersymmetric positive definite scalar products together with natural Krein structures of supersymmetries.

Banach spaces have been given by Edelstein but under hypotheses on the existence of strong limit points for the sequence I Unx I which are difficult to verify. Cf. Edelstein, M., "On fixed and periodic points under contractive mappings," J. London Math. Soc., 37, 74-79 (1962), "On nonexpansive mappings of Banach spaces," Proc. Cambridge Philos. Soc., 60, 439-447 (1964). 9 Added in proof: After ...

It was shown that quantum metric fluctuations smear out the singularities of Green’s functions on the light cone [1], but it does not remove other ultraviolet divergences of quantum field theory. We have proved that the quantum field theory in Krein space, i.e. indefinite metric quantization, removes all divergences of quantum field theory with exception of the light cone singularity [2, 3]. In...

Let à be a self-adjoint extension in K̃ of a fixed symmetric operator A in K ⊆ K̃. An analytic characterization of the eigenvalues of à is given in terms of the Q-function and the parameter function in the Krein–Naimark formula. Here K and K̃ are Krein spaces and it is assumed that à locally has the same spectral properties as a self-adjoint operator in a Pontryagin space. The general results are ...

In this paper, we study the finite horizon H∞ fixed-lag smoothing problem for linear descriptor systems. The key approach applied for deriving the H∞ fixed-lag smoother is the re-organization innovation analysis in Krein space. Under the Krein space, the H∞ fixed-lag smoothing is converted into an H2 estimation problem for the system with current and delayed measurements. By using innovation re...

It is well known that RN has subspaces of dimension proportional to N on which the l1 norm is equivalent to the l2 norm; however, no explicit constructions are known. Extending earlier work by Artstein– Avidan and Milman, we prove that such a subspace can be generated using O(N) random bits.

Let 5 and 8 be Krein spaces. By S(3 ,8 ) we denote the (generalized Schur) class of all functions O, defined and holomorphic at z = 0 and with values in L(5,8), the space of bounded Linear operators from 5 to 8 (we write L ( 8 ) for L(3,S)). It is known, see Section 3 below, that any OeS(3,8) is in some neighborhood of z = 0 the characteristic function On of a unitary colligation A = (J?,S,@;U)...

This paper addresses the H , fixed-lag smoothing and prediction problems for linear continuous-time systems. We first present a solution to the optimal HZ estimation problem for linear continuous-time systems with instantaneous and delayed measurements. It is then shown that the H , fixedlag smoothing and prediction problems can be converted to the latter problem in Krein space. Therefore, the ...