caa a22 4500 605495912 CHVBK 20210128100533.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10231-013-0369-z doi (NATIONALLICENCE)springer-10.1007/s10231-013-0369-z Seiler Jörg Dipartimento di Matematica, Università di Torino, 10123, Torino, Italy aut Parameter-dependent pseudodifferential operators of Toeplitz type [Elektronische Daten] [Jörg Seiler] We present a calculus of pseudodifferential operators that contains both usual parameter-dependent operators—where a real parameter $$\tau $$ τ enters as an additional covariable—as well as operators not depending on $$\tau $$ τ . Parameter-ellipticity is characterized by the invertibility of three associated principal symbols. The homogeneous principal symbol is not smooth on the whole cosphere bundle but only admits directional limits at the north-poles, encoded by a principal angular symbol. Furthermore, there is a limit-family for $$\tau \rightarrow +\infty $$ τ → + ∞ . Ellipticity permits to construct parametrices that are inverses for large values of the parameter. We then obtain subcalculi of Toeplitz type with a corresponding symbol structure. In particular, we discuss invertibility of operators of the form $$P_1A(\tau )P_0$$ P 1 A ( τ ) P 0 where both $$P_0$$ P 0 and $$P_1$$ P 1 are zero-order projections and $$A(\tau )$$ A ( τ ) is a usual parameter-dependent operator of arbitrary order or $$A(\tau )=\tau ^{\mu }-A$$ A ( τ ) = τ μ - A with a pseudodifferential operator $$A$$ A of positive integer order $$\mu $$ μ . Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 Parameter-dependent pseudodifferential operators nationallicence Operators of Toeplitz type nationallicence Parametrix nationallicence Resolvent nationallicence Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/1(2015-02-01), 145-165 0373-3114 194:1<145 2015 194 10231 https://doi.org/10.1007/s10231-013-0369-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-013-0369-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Seiler Jörg Dipartimento di Matematica, Università di Torino, 10123, Torino, Italy aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/1(2015-02-01), 145-165 0373-3114 194:1<145 2015 194 10231