ausgewiesen
recognized
Recognized and known as an expert or specialist in a particular field.
Er ist ein ausgewiesener Kenner der modernen Kunst.
He is a recognized expert on modern art.

recognized / designated / stated / expelled
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recognized
Recognized and known as an expert or specialist in a particular field.
Er ist ein ausgewiesener Kenner der modernen Kunst.
He is a recognized expert on modern art.

'Ausgewiesen' (recognized/designated/stated/expelled) is the past participle of the separable verb 'ausweisen' (to identify; to designate; to expel). It is used like an adjective and usually stands directly before a noun.
Das ist ein ausgewiesenes Naturschutzgebiet.
This is a designated nature reserve.
You can recognize the meaning from the noun: If 'ausgewiesen' refers to a person, they are either an expert or have been expelled from the country. If it refers to a place, it is designated. If it refers to numbers, they are officially stated.
Er ist ein ausgewiesener Experte für Wein.
He is a recognized expert on wine.
In the meaning 'expert', 'ausgewiesen' (recognized) is almost always combined with nouns that describe a person with special knowledge. Typical phrases are 'ausgewiesener Experte' (recognized expert), 'ausgewiesener Fachmann' (recognized specialist), or 'ausgewiesener Kenner' (recognized connoisseur/expert).
Für die Reparatur brauchen wir einen ausgewiesenen Fachmann.
For the repair, we need a recognized specialist.
When something is officially marked, 'ausgewiesen' (designated) is often used for zones and areas. Common combinations are 'ausgewiesene Parkplätze' (designated parking spaces), 'ausgewiesene Raucherbereiche' (designated smoking areas), or 'ausgewiesene Hundezonen' (designated dog zones).
Rauchen ist nur in den ausgewiesenen Bereichen gestattet.
Smoking is only permitted in the designated areas.
You will find this meaning almost exclusively in business and financial texts. The word refers to figures in official documents such as balance sheets, annual reports, or invoices.
Der ausgewiesene Umsatz übertraf alle Erwartungen.
The stated revenue exceeded all expectations.
certain / specific
'bestimmt' and 'ausgewiesen' can both mean that something is intended for a specific purpose. 'bestimmt für' (intended for) is more general: something is meant for a person, a group, or a purpose. 'ausgewiesen' sounds more official and usually means that something is clearly marked or officially designated, for example by a sign, a plan, or a document. The words can be confused because both express a purpose. When it is about an official designation or marking, 'ausgewiesen' is more precise.

Der Bereich vor dem Gebäude ist als Parkplatz für Besucher ausgewiesen.
The area in front of the building is designated as visitor parking.
Diese Plätze sind für ältere Fahrgäste bestimmt.
These seats are intended for older passengers.