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Context. Debris disks are commonly considered to be a by-product of planet formation. Structures in debris disks induced by planet-disk interaction are promising to provide valuable constraints on the existence and properties of embedded planets. Aims. We investigate the observability of structures in debris disks induced by planet-disk interaction with future facilities in a systematic way. High-sensitivity, high angular resolution observations with large (sub-)mm interferometers and large space-based telescopes operating in the near- to mid-infrared wavelength range are considered. Methods. The observability of debris disks with the Atacama LargeMillimeter/submillimeter Array (ALMA) is studied on the basis of a simple analytical disk model. Furthermore, N-body simulations are used to model the spatial dust distribution in debris disks under the influence of planet-disk interaction. From these simulations, images at optical scattered light to millimeter thermal re-emission are computed. Available information about the expected capabilities of ALMA and the James Webb Space Telescope (JWST) are used to investigate the observability of characteristic disk structures with these facilities through spatially resolved imaging. Results. Our simulations show that planet-disk interaction can result in prominent structures in the whole considered wavelength range. The exact result depends on the configuration of the planet-disk system and on the observing wavelength which provides the opportunity of detecting and characterizing extrasolar planets in a range of masses and radial distances from the star that is not accessible to other techniques. Facilities that will be available in the near future at both considered wavelength ranges are shown to provide the capabilities to spatially resolve and characterize structures in debris disks that arise because of planet-disk interaction. Limitations are revealed and suggestions for possible instrument setups and observing strategies are given. In particular, ALMA is limited by its sensitivity to surface brightness, which requires a trade-off between sensitivity and spatial resolution. Space-based midinfrared observations will be able to detect and spatially resolve regions in debris disks even at a distance of several tens of AU from the star, where the emission from debris disks in this wavelength range is expected to be low. Conclusions. Both ALMA and the planned space-based near- to mid-infrared telescopes will provide unprecedented capabilities to study planet-disk interaction in debris disks. In particular, a combination of observations at both wavelengths will provide very strong constraints on the planetary/planetesimal systems. [ABSTRACT FROM AUTHOR]